ICSE

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 15 Decimal Fractions

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 15 Decimal Fractions

Decimal Fractions Exercise 15A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Write the number of decimal places in each of the following :
(i) 7.03
(ii) 0.509
(iii) 146.2
(iv) 0.0065
(v) 8.03207
Solution:

Question 2.
Convert the given unlike decimal fractions into like decimal fractions:
(i) 1.36, 239.8 and 47.008
(ii) 507.0752, 8.52073 and 0.808
(iii) 459.22, 7.03093 and 0.200037
Solution:

Question 3.
Change each of following fractions to a decimal fraction :

Solution:

Question 4.
Convert into a decimal fraction :

Solution:

Question 5.
Change the given decimals fractions to fractions in their lowest terms :
(i) 0.05
(ii) 3.95
(iii) 4.005
(iv) 0.876
(v) 50.06
(vi) 0.01075
(vii) 4.8806
Solution:

Decimal Fractions Exercise 15B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Add the following :
(i) 0.243, 2.47 and 3.009
(ii) 0.0736, 0.6095 and 0.9107
(iii) 1.01, 257 and 0.200
(iv) 18, 200.35, 11.72 and 2.3
(v) 0.586, 0.0586 and 0.00586
Solution:

Question 2.
Find the value of :
(i) 6.8 – 2.64
(ii) 2 – 1.0304
(iii) 0.1 – 0.08
(iv) 0.83 – 0.342
Solution:

Question 3.
Subtract :
(i) 0.43 from 0.97
(ii) 2.008 from 22.1058
(iii) 0.18 from 0.6
(iv) 1.002 from 17
(v) 83 from 92.05
Solution:

Question 4.
Simplify :
(i) 3.5 – 2.43 + 0.075
(ii) 7.84 + 0.3 – 4.016
(iii) 2.987 – 1.25 – 0.54
(iv) 52.9 – 231.666 + 204
(v) 8.57 – 6.4432 – 1.70 + 0.683
Solution:

Question 5.
From the sum of 75.75 and 4.9 subtract 28.465.
Solution:

Question 6.
Subtract the sum of 8.14 and 12.9 from 32.7.
Solution:

Question 7.
Subtract the sum of 34.27 and 159.8 from the sum of 20.937 and 200.6.
Solution:

Question 8.
From the sum of 2.43 and 4.349 subtract the sum of 0.8 and 3.15.
Solution:

Question 9.
By how much does the sum of 18.0495 and 34.9644 exceed the sum of 7.6752 and 24.876?
Solution:

Question 10.
What least number must be added to 89.376 to get 1000?
Solution:

Decimal Fractions Exercise 15C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Multiply :
(i) 5.6 and 8
(ii) 38.46 and 9
(iii) 0.943 and 62
(iv) 0.0453 and 35
(v) 7.5 and 2.5
(vi) 4.23 and 0.8
(vii) 83.54 and 0.07
(viii) 0.636 and 1.83
(ix) 6.4564 and 1000
(x) 0.076 and 100
Solution:

Question 2.
Evaluate :
(i) 0.0008 x 26
(ii) 0.038 x 95
(iii) 1.2 x 2.4 x 3.6
(iv) 0.9 x 1.8 x 0.27
(v) 1.5 x 1.5 x 1.5
(vi) 0.025 x 0.025
(vii) 0.2 x 0.002 x 0.001
Solution:

Question 3.
Multiply each of the following numbers by 10, 100 and 1000 :
(i) 3.9
(ii) 2.89
(in) 0.0829
(iv) 40.3
(v) 0.3725
Solution:

Question 4.
Evaluate :
(i) 8.64 ÷ 8
(ii) 0.0072 ÷ 6
(iii) 20.64 ÷ 16
(iv) 1.602 ÷ 15
(v) 13.08 ÷ 4
(vi) 3.204 ÷ 9
(vii) 3.024 ÷ 12
(viii) 5.15 ÷ 5
(ix) 3 ÷ 5
Solution:

Question 5.
Divide each of the following numbers by 10,100 and 1000 :
(i) 49.79
(ii) 0.923
(iii) 0.0704
Solution:

Question 6.
Evaluate :
(i) 9.4 ÷ 0.47
(ii) 6.3 ÷ 0.09
(iii) 2.88 ÷ 1.2
(iv) 8.64 ÷ 1.6
(v) 37.188 ÷ 3.6
(vi) 16.5 ÷ 0.15
(vii) 3.2 ÷ 0.005
(viii) 3.24 ÷ 0.0016
Solution:

Question 7.
Fill in the blanks with 10,100,1000, or 10000 etc.:
(i) 7.85 x ………….. = 78.5
(ii) 0.442 x ………. = 442
(in) 0.0924 x ………… = 9.24
(iv) 0.00187 x …………. = 18-7
(v) 2.6 x …………. = 2600
(vi) 0.08 x ………… = 80
(vii) 96.7 ÷ ………….. = 0.967
(viii) 5.2 ÷ ……………. = 0.52
(ix) 33.15 ÷ ……………….. = 0.03315
(x) 0.7 ÷ ………… = 0.007
(xi) 0.00672 x ……… = 67.2
Solution:

Question 8.
Evaluate :
(i) 9.32 – 28.54 ÷ 10
(ii) 0.234 x 10 + 62.8
(iii) 3.06 x 100 – 889.4 ÷ 100
(iv) 2.86 x 7.5 + 45.4 ÷ 0.2
(v) 97.82 x 0.03 – 0.54 ÷ 0.3
Solution:

Decimal Fractions Exercise 15D – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Express in paise :
(i) Rs. 8.40
(ii) Rs. 0.97
(iii) Rs. 0.09
(iv) Rs. 62.35
Solution:

Question 2.
Express in rupees :
(i) 55 P
(ii) 8 P
(iii) 695 P
(iv) 3279 P
Solution:

Question 3.
Express in centimetre (cm) :
(i) 6 m
(ii) 8.54 m
(iii) 3.08 m
(iv) 0.87 m
(v) 0.03 m
(vi) 25.04 m
Solution:

Question 4.
Express in metre (m) :
(i) 250 cm
(ii) 2328 cm
(iii) 86 cm
(iv) 4 cm
(v) 107 cm
Solution:

Question 5.
Express in gramme (gm) :
(i) 6 kg
(ii) 5.543 kg
(iii) 0.078 kg
(iv) 3.62 kg
(v) 4.5 kg
Solution:

Question 6.
Express in kilogramme (kg) :
(i) 7000 gm
(ii) 6839 gm
(iii) 445 gm
(iv) 8 gm
(iv) 93 gm
(vi) 13545 gm
Solution:

Question 7.
Add (giving answer in rupees) :
(i) Rs. 5.37 and Rs. 12
(ii) Rs. 24.03 and 532 paise
(iii) 73 paise and Rs. 208
(iv) 8 paise and Rs. 1536
Solution:

Question 8.
Subtract :
(i) Rs. 35.74 from Rs. 63.22
(ii) 286 paise from Rs. 7.02
(iii) Rs. 0.55 from 121 paise
Solution:

Question 9.
Add (giving answer in metre) :
(i) 2.4 m and 1.78 m
(ii) 848 cm and 2.9 m
(iii) 0.93 m and 64 cm
Solution:

Question 10.
Subtract (giving answer in metre) :
(i) 5.03 m from 19.6 m
(ii) 428 cm from 1033 m
(iii) 0.84 m from 122 cm
Solution:

Question 11.
Add (giving answer in kg) :
(i) 2.06 kg and 57.864 kg
(ii) 778 gm and 1.939 kg
(iii) 0.065 kg and 4023 gm
Solution:

Question 12.
Subtract (giving answer in kg) :
(i) 9.462 kg from 15.6 kg
(ii) 4317 gm from 23 kg
(iii) 0.798 kg from 4169 gm
Solution:

Decimal Fractions Exercise 15E – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
The cost of a fountain pen is Rs. 13.25. Find the cost of 8 such pens.
Solution:

Question 2.
The cost of 25 identical articles is Rs. 218.25. Find the cost of one article.
Solution:

Question 3.
The length of an iron rod is 10.32 m. The rod is divided into 4 pieces of equal lengths. Find the length of each piece.
Solution:

Question 4.
What will be the total length of cloth required to make 5 shirts, if 2.15 m of cloth is needed for each shirt?
Solution:

Question 5.
Find the distance walked by a boy in 1\(\frac { 1 }{ 2 }\) hours, if he walks at 2.150 km every hour.
Solution:

Question 6.
83 note-books are sold at Rs. 15.25 each. Find the total money (in rupees) obtained by selling these note-books.
Solution:

Question 7.
If length of one bed-cover is 2.1 m, find the total length of 17 bed-covers.
Solution:

Question 8.
A piece of rope is 10 m 67 cm long. Another rope is 16 m 32 cm long. By how much is the second rope longer than the first one?
Solution:

Question 9.
12 cakes of soap together weigh 5 kg and 604 gm. Find the weight of
(i) One cake in both kg and gramme
(ii) 5 cakes in kg.
Solution:

Question 10.
Three strings of lengths 50 m 75 cm; 68 m 58 cm and 121 m 3 cm, respectively, are joined together to get a single string of greatest length, And the length of the single string obtained.
If this single string is then divided into 12 equal pieces ; find the length of each piece.
Solution:

Decimal Fractions Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Write th& following decimal numbers in ascending order of value
(i) 5.054, 5.250, 5.245 and 5.0543
(ii) 62.443, 62.434, 62.344 and 62.444
Solution:

Question 2.
What number added to 0.805 gives 1?
Solution:

Question 3.
What must be subtracted from 3 to get 2.462?
Solution:

Question 4.
By how much should 83.407 be decreased to get 27.78?
Solution:

Question 5.
Two articles weigh 32.674 kg and 40.038 kg respectively. Find :
(i) the total weight of both the articles.
(ii) the difference in the weights of both the articles.
Solution:

Question 6.
By how much does the sum of 34.07 and 15.239 exceed the sum of 16.40 and 27.08?
Solution:

Question 7.
The cost of 1 kg of fruit is Rs. 27.50. What is the cost of 3.6 kg of fruit?
Solution:

Question 8.
Evaluate :
(i) 0.8 x 0.8 x 0.8
(ii) 0.8 ÷ 0.8 x 0.8
(iii) 0.8 x 0.8 ÷ 0.8
(iv) 0.8 ÷ 0.8 of 0.8
(v) 0.8 of 0.8 ÷ 0.8
Solution:

Question 9.
Evaluate :
(i) 3.5 x (4.2 + 2.6)
(ii) 3.5 x 4.2 + 3.5 x 2.6
Are (i) and (ii) equal ?
Solution:

Question 10.
Evaluate :
(i) (3.87 – 2.09) x 2.4
(ii) 3.87 x 2.4 – 2.09 x 2.4
Are (i) and (ii) equal ?
Solution:

Question 11.
A 4.85 m long pole is divided into 5 equal parts. Find the length of each part.
Solution:

Question 12.
A car can run 16.8 km consuming one litre of petrol. How many kilometres will it run on 3.7 litres of petrol ?
Solution:

Question 13.
A certain amount of money is distributed among 28 persons. If each person gets Rs. 62.45 and Rs. 5.78 is left, find the original amount of money.
Solution:

Question 14.
Complete the following table :

Solution:

Question 15.
The difference between two numbers is 47.364. If the smaller number is 31.855 ; find the bigger one.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 14 Fractions

Fractions Exercise 14A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
For each expression, given below, write a fraction :
(i) 2 out of 7 = ………..
(ii) 5 out of 17 = ………..
(iii) three-fifths = ………
Solution:

Question 2.
Fill in the blanks :


Solution:

Question 3.
From the following fractions, separate :
(i) Proper fractions
(ii)Improper fractions :

Solution:

Question 4.
Change the following mixed fractions to improper fractions :

Solution:

Question 5.
Change the following improper fractions to mixed fractions :

Solution:

Question 6.
Change the following groups of fractions to like fractions :

Solution:

Fractions Exercise 14B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Reduce the given fractions to their lowest terms :

Solution:

Question 2.
State, whether true or false?

Solution:

Question 3.
Which fraction is greater?

Solution:
<

Question 4.
Which fraction is smaller ?

Solution:

Question 5.
Arrange the given fractions in descending order of magnitude :

Solution:
<

Question 6.
Arrange the given fractions in ascending order of magnitude :

Solution:

Question 7.
I bought one dozen bananas and ate five of them. What fraction of the total number of bananas was left ?
Solution:

Question 8.
Insert the symbol ‘=’ or ‘>’ or ‘<’ between each of the pairs of fractions, given below :

Solution:

Question 9.
Out of 50 identical articles, 36 are broken. Find the fraction of :
(i) The total number of articles and the articles broken.
(ii) The remaining articles and total number of articles.
Solution:

Fractions Exercise 14C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Add the following fractions :

Solution:

Question 2.
Simplify :

Solution:

Fractions Exercise 14D – Selina Concise Mathematics Class 6 ICSE Solutions

Point to Remember :
BODMAS :- While simplifying an expressions we can involve six operation in following orders.
B Stands for “BRACKET”
O Stands for “OF”
D Stands for “DIVISION”
M Stands for “MULTIPLICATION”
A Stands for “ADDITION”
S Stands for “SUBTRACTION”

Question 1.
Simplify :

Solution:

Question 2.
Simplify :

Solution:

Question 3.
Simplify :

Solution:

Question 4.
Simplify :


Solution:

Question 5.
Simplify :


Solution:

Fractions Exercise 14E – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
From a rope of 10\(\frac { 1 }{ 2 }\) m long, 4\(\frac { 5 }{ 8 }\) m is cut off. Find the length of the remaining rope.
Solution:

Question 2.
A piece of cloth is 5 metre long. After washing, it shrinks by \(\frac { 1 }{ 25 }\) of its length. What is the length of the cloth after washing?
Solution:

Question 3.
I bought wheat worth Rs. 12\(\frac { 1 }{ 2 }\), rice worth Rs. 25\(\frac { 3 }{ 4 }\) and vegetables worth Rs. 10\(\frac { 1 }{ 4 }\). If I gave a hundred-rupee note to the shopkeeper ; how much did he return to me
Solution:

Question 4.
Out of 500 oranges in a box, \(\frac { 3 }{ 25 }\) are rotten and \(\frac { 1 }{ 5 }\) are kept for some guests. How many oranges are left in the box?
Solution:

Question 5.
An ornament piece is made of gold and copper. Its total weight is 96g. If \(\frac { 1 }{ 12 }\) of the ornament hi copper, find the weight of gold in it.
Solution:

Question 6.
A girl did half of some work on Monday and one-third of it on Tuesday. How much will she have to do on Wednesday in order to complete the work?
Solution:

Question 7.
A man spends \(\frac { 3 }{ 8 }\) of his money and 8 still has Rs. 720 left with him. How much money did he have at first?
Solution:

Question 8.
In a school, \(\frac { 4 }{ 5 }\) of the students are boys, and the number of girls is 100. Find the number of boys.
Solution:

Question 9.
After finishing \(\frac { 3 }{ 4 }\) of my journey, I find that 12 km of my journey is covered. How much distance is still left to be covered?
Solution:

Question 10.
When Ajit travelled 15 km, he found that one-fourth of his journey was still left. What was the full length of the journey?
Solution:

Question 11.
In a particular month, a man earns Rs. 7,200. Out of this income, he spends \(\frac { 3 }{ 10 }\) on food, \(\frac { 1 }{ 4 }\) on house rent, \(\frac { 1 }{ 10 }\) on insurance and \(\frac { 2 }{ 25 }\) on holidays. How much did he save in that month ?
Solution:

Fractions Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.

Solution:

Question 2.

Solution:

Question 3.
Evaluate :

Solution:

Question 4.
Mr. Mehra gave one-third of his money to his son, one-fifth of his money to his daughter and the remaining amount to his wife. If his wife got Rs. 91,000, how much money did Mr. Mehra have originally?
Solution:

Question 5.
A sum of Rs. 84,000 is divided among three persons A, B and C. If A gets one-fourth of it and B gets one-fifth of it; how much did C get?
Solution:

Question 6.
In one hour Rohit walks 3\(\frac { 2 }{ 5 }\) km. How much distance will he cover in 2\(\frac { 1 }{ 2 }\) hours?
Solution:

Question 7.
An 84 m long string is cut into pieces each of length 5\(\frac { 1 }{ 4 }\) m. How many pieces are obtained?
Solution:

Question 8.
In buying a ready made shirt-two-fifths of my pocket money is spent If Rs. 540 is still left with me, find :
(i) The money I had before I bought the shirt.
(ii) The emit of the shirt
Solution:

Question 9.
Mohan leaves Rs. 1,20,000 to his wife and three children such that two-fifths of this money is given to his wife and the remaining is distributed equally among the children. Find, how much each child gets?
Solution:

Question 10.
Simplify :

Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 2 Rational Numbers

Rational Numbers Exercise 2A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Write down a rational number whose numerator is the largest number of two digits and denominator is the smallest number of four digits.

Solution:

Question 2.
Write the numerator of each of the following rational numbers:

Solution:

Question 3.
Write the denominator of each of the following rational numbers:

Solution:

Question 4.
Write down a rational number numerator (-5) x (-4) and denominator (28 – 27) x (8 – 5).

Solution:

Question 5.

Solution:

Question 6.
Separate positive and negative rational numbers from the following :

Solution:

Question 7.
Find three rational numbers equivalent to

Solution:

Question 8.
Which of the following are not rational numbers :

Solution:

Question 9.
Express each of the following integers as a rational number with denominator 7 :
(i) 5
(ii) -8
(iii) 0
(iv) -16
(v) 7
Solution:

Question 10.
Express \(\frac { 3 }{ 5 }\) as a rational number with denominator:
Solution:

Question 11.
Express \(\frac { 4 }{ 7 }\) as a rational number with numerator :
Solution:

Question 12.
Find x, such that:

Solution:

Question 13.
Express each of the following rational numbers to the lowest terms :

Solution:

Question 14.
Express each of the following rational numbers in the standard form.

Solution:

Rational Numbers Exercise 2B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Mark the following pairs of rational numbers on the separate number lines :

Solution:

Question 2.
Compare:

Solution:

Question 3.
Compare:

Solution:

Question 4.
Arrange the given rational numbers in ascending order :

Solution:

Question 5.
Arrange the given rational numbers in descending order:

Solution:

Question 6.
Fill in the blanks :

Solution:

Rational Numbers Exercise 2C – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Add:

Solution:

Question 2.
Add:

Solution:

Question 3.
Evaluate:

Solution:

Question 4.
Evaluate:

Solution:

Question 5.
Subtract :

Solution:

Question 6.
Subtract :

Solution:

Question 7.
The sum of two rational numbers is \(\frac { 11 }{ 24 }\). If one of them is \(\frac { 3 }{ 8 }\), find the other.
Solution:

Question 8.
The sum of two rational numbers is \(\frac { -7 }{ 11 }\). If one of them is \(\frac { 13 }{ 24 }\), find the other.
Solution:

Question 9.
The sum of two rational numbers is -4. If one of them is \(-\frac { 13 }{ 12 }\) , find the other.
Solution:

Question 10.
What should be added to \(-\frac { 3 }{ 6 }\) to get \(-\frac { 11 }{ 24 }\) ?
Solution:

Question 11.
What should be added to \(\frac { -3 }{ 5 }\) to get 2?
Solution:

Question 12.
What should be subtracted from \(\frac { -4 }{ 5 }\) to get 1?
Solution:

Question 13.
The sum of two numbers is \(-\frac { 6 }{ 5 }\). If one of them is -2, find the other.
Solution:

Question 14.
What should be added to \(\frac { -7 }{ 12 }\) to get \(\frac { 3 }{ 8 }\)?

Solution:

Question 15.
What should be subtracted from \(\frac { 5 }{ 9 }\)to get \(\frac { 9 }{ 5 }\) ?
Solution:

Rational Numbers Exercise 2D – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Evaluate:

Solution:

Question 2.
Multiply:

Solution:

Question 3.
Evaluate:


Solution:

Question 4.
Find the cost of 3 \(\frac { 1 }{ 2 }\) m cloth, if one metre cloth costs ₹325 \(\frac { 1 }{ 2 }\).
Solution:

Question 5.
A bus is moving with a speed of 65 \(\frac { 1 }{ 2 }\) km per hour. How much distance will it cover in 1 \(\frac { 1 }{ 3 }\) hours.
Solution:

Question 6.
Divide:

Solution:

Question 7.
Evaluate:

Solution:

Question 8.
The product of two numbers is 14. If one of the numbers is \(\frac { -8 }{ 7 }\), find the other.
Solution:

Question 9.
The cost of 11 pens is ₹3 \(\frac { 2 }{ 3 }\). Find the cost of one pen.
Solution:

Question 10.
If 6 identical articles can be bought for ₹2 \(\frac { 6 }{ 17 }\). Find the cost of each article.
Solution:

Question 11.
By what number should \(\frac { -3 }{ 8 }\) be multiplied so that the product is \(\frac { -9 }{ 16 }\) ?
Solution:

Question 12.
By what number should \(\frac { -5 }{ 7 }\) be divided so -15 that the result is\(\frac { -15 }{ 28 }\) ?
Solution:

Question 13.
Evaluate :

Solution:

Question 14.
Seven equal piece are made out of a rope 5 of 21 \(\frac { 5 }{ 7 }\) m. Find the length of each piece.
Solution:

Rational Numbers Exercise 2E – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Evaluate:

Solution:

Question 2.
The sum of two rational numbers is \(\frac { -3 }{ 8 }\). If one of them is \(\frac { 3 }{ 16 }\), find the other,
Solution:

Question 3.
The sum of two rational numbers is -5. If one of them is \(\frac { -52 }{ 25 }\) , find the other.
Solution:

Question 4.
What rational number should be added to \(-\frac { 3 }{ 16 }\) to get \(\frac { 11 }{ 24 }\)
Solution:

Question 5.
What rational number should be added to \(-\frac { 3 }{ 5 }\) to get 2?
Solution:

Question 6.
What rational number should be subtracted from \(-\frac { 5 }{ 12 }\)to get \(\frac { 5 }{ 24 }\)
Solution:

Question 7.
What rational number should be subtracted from \(\frac { 5 }{ 8 }\) to get \(\frac { 8 }{ 5 }\) ?
Solution:

Question 8.
Evaluate:

Solution:




Question 9.
The product of two rational numbers is 24. If one of them is \(-\frac { 36}{ 11 }\), find the other.
Solution:

Question 10.
By what rational number should we multiply \(\frac { 20 }{ -9 }\) ,so that the product may be \(\frac { -5 }{ 9 }\) ?
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method

Unitary Method Exercise 13A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
The price of 25 identical articles is ₹ 1,750. Find the price of :
(i) one article
(ii) 13 articles
Solution:

Question 2.
A motorbike travels 330 km in 5 litres of petrol. How much distance will it cover in :
(i) one litre of petrol?
(ii) 2.5 litres of petrol?
Solution:

Question 3.
If the cost of a dozen soaps is ₹ 460.80, what will the cost of:
(i) each soap?
(ii) 15 soaps?
(iii) 3 dozen soaps?
Solution:

Question 4.
The cost of 35 envelops is ₹ 105. How many envelops can be bought for ₹ 90?
Solution:

Question 5.
If the cost of 8 cans of juice is ₹ 280, then what will be the cost of 6 cans of juice?
Solution:

Question 6.
For ₹ 378, 9 cans of juice can be bought, then how many cans of juice can be bought for ₹ 504?
Solution:

Question 7.
A motorbike travels 425 km in 5 hours. How much distance will be covered by it in 3.2 hours?
Solution:

Question 8.
If the cost of a dozen identical articles is ₹ 672, what will be the cost of 18 such articles?
Solution:

Question 9.
A car covers a distance of 180 km in 5 hours.
(i) How much distance will the car cover in 3 hours with the same speed ?
(ii) How much time will the car take to cover 54 km with the same speed?
Solution:

Question 10.
If it has rained 276 cm in the last 3 days, how many cm of rain will fall in one week (7 days) ?
Assume that the rain continues to fall at the same rate.
Solution:

Question 11.
Cost of 10 kg of wheat is ₹ 180.
(i) What is the cost of 18 kg of wheat?
(ii) What quantity of wheat can be purchased in ₹ 432?
Solution:

Question 12.
Rohit buys 10 pens for ₹ 150 and Manoj buys 14 pens for ₹ 168. Who got the pens cheaper?
Solution:

Question 13.
A tree 24 m high casts a shadow of 15 m. At the same time, the length of the shadow casted by some other tree is 6 m. Find the height of the tree.
Solution:

Question 14.
A loaded truck travels 18 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours?
Solution:

Unitary Method Exercise 13B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Weight of 15 books is 6 kg. What is the weight of 45 such books?
Solution:

Question 2.
A made 84 runs in 6 overs and B made 126 runs in 7 overs. Who made more runs per over?
Solution:

Question 3.
Geeta types 108 words in 6 minutes. How many words would she type in half an hour?
Solution:

Question 4.
The temperature dropped 18 degree Celsius in the last 24 days. If the rate of temperature drop remains the same, how many degrees will the temperature drop in the next 18 days?
Solution:

Question 5.
Mr. Chopra pays ₹ 12,000 as rent for 3 months. How much does he has to pay for a year if the rent per month remains same?
Solution:

Question 6.
A truck requires 108 litres of diesel for covering a distance of 1188 km. How much diesel will be required by the truck to cover a distance of 3300 km?
Solution:

Question 7.
If a deposit of ₹ 2,000 earns an interest of ₹ 500 in 3 years, how much interest would a deposit of ₹ 36,000 earn in 3 years with the same rate of simple interest?
Solution:

Question 8.
If John walks 250 steps to cover a distance of 200 metres, find the distance covered by him in 350 steps.
Solution:

Question 9.
25 metres of cloth costs ₹ 1,012.50.
(i) What will be the cost of 20 metres of cloth of the same type?
(ii) How many metres of the same kind can be bought for ₹ 1,620?
Solution:

Question 10.
In a particular week, a man works for 48 hours and earns ₹ 4,320. But in the next week he worked 6 hours less, how much has he earned in this week?
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion (Including Word Problems)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion (Including Word Problems)

Proportion Exercise 12A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
In each of the following, check whether or not the given ratios form a proportion :
(i) 8 : 16 and 12 : 15
(ii) 16 : 28 and 24 : 42
(iii) 12 ÷ 3 and 8 ÷ 2
(iv) 25 : 40 and 20 : 32
(v) \(\frac { 15 }{ 18 }  and \frac { 10 }{ 12 }\)
(vi) \(\frac { 7 }{ 8 }\) and 14 : 16
Solution:

Question 2.
Find the value of x in .each of the following proportions :
(i) x : 4 = 6 : 8
(ii) 14 : x = 7 : 9
(iii) 4 : 6 = x : 18
(iv) 8 : 10 = x : 25
(v) 5 : 15 = 4 : x
(vi) 16 : 24 = 6 : x
Solution:

Question 3.
Find the value of x so that the given four numbers are in proportion :
(i) x, 6, 10 and 15
(ii) x, 4, 15 and 30
(iii) 2, x, 10 and 25
(iv) 4, x, 6 and 18
(v) 9, 12, x and 8
(vi) 4, 10, 36 and x
(vii) 7, 21, x and 45
(viii) 6, 8, 12 and x.
Solution:

Question 4.
The first, second and the fourth terms of a proportion are 6, 18 and 75, respectively. Find its third term.
Solution:

Question 5.
Find the second term of the proportion whose first, third and fourth terms are 9, 8 and 24 respectively.
Solution:

Question 6.
Find the fourth term of the proportion whose first, second and third terms are 18, 27, and 32 respectively.
Solution:

Question 7.
The ratio of the length and the width of a school ground is 5 : 2. Find the length, if the width is 40 metres.
Solution:

Question 8.
The ratio of the sale of eggs on a Sunday and that of the whole week at a grocery shop was 2 : 9. If the total value of the sale of eggs in the same week was Rs 360, find the value of the sale of eggs that Sunday.
Solution:

Question 9.
The ratio of copper and zinc in an alloy is 9 : 8. If the weight of zinc, in the alloy, is 9.6 kg ; find the weight of copper in the alloy.
Solution:

Question 10.
The ratio of the number of girls to the number of boys in a school is 2 : 5. If the number of boys is 225 ; find:
(i) the number of girls in the school.
(ii) the number of students in the school.
Solution:

Question 11.
In a class, one out of every 5 students pass. If there are 225 students in all the sections of a class, find how many pass ?
Solution:

Question 12.
Make set of all possible proportions from the numbers 15, 18, 35 and 42.
Solution:

Proportion Exercise 12B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
If x, y and z are in continued proportion, then which of the following is true :
(i) x : y = x : z
(ii) x : x = z : y
(iii) x : y = y : z
(iv) y : x = y : z
Solution:

Question 2.
Which of the following numbers are in continued proportion :
(i) 3, 6 and 15
(ii) 15, 45 and 48
(iii) 6, 12 and 24
(iv) 12, 18 and 27
Solution:

Question 3.
Find the mean proportion between
(i) 3 and 27
(ii) 0.06 and 0.96
Solution:

Question 4.
Find the third proportional to :
(i) 36, 18
(ii) 5.25, 7
(iii) ₹ 1.60, ₹ 0.40
Solution:

Question 5.
The ratio between 7 and 5 is same as the ratio between ₹ x and ₹ 20.50 ; find the value of x.
Solution:

Question 6.
If (4x + 3y) : (3x + 5y) = 6 : 7, find :
(i) x : y
(ii) x, if y = 10
(iii) y, if x = 27
Solution:
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Question 7.
If \(\frac { 2y+5x }{ 3y-5x } =2\frac { 1 }{ 2 }\), find:
(i) x : y
(ii) x, if y = 70
(iii) y, if x = 33
Solution:

Proportion Exercise 12C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Are the following numbers in proportion:
(i) 32, 40, 48 and 60 ?
(ii) 12,15,18 and 20 ?
Solution:

Question 2.
Find the value of x in each of the following such that the given numbers are in proportion.
(i) 14, 42, x and 75
(ii) 45, 135, 90 and x
Solution:

Question 3.
The costs of two articles are in the ratio 7 : 4. If the cost of the first article is Rs. 2,800 ; find the cost of the second article.
Solution:

Question 4.
The ratio of the length and the width of a rectangular sheet of paper is 8 : 5. If the width of the sheet is 17.5 cm; find the length.
Solution:

Question 5.
The ages of A and B are in the ratio 6 : 5. If A’s age is 18 years, find the age of B.
Solution:

Question 6.
A sum of Rs. 10, 500 is divided among A, B and C in the ratio 5 : 6 : 4. Find the share of each.
Solution:

Question 7.
Do the ratios 15 cm to 2 m and 10 sec to 3 minutes form a proportion ?
Solution:

Question 8.
Do the ratios 2 kg : 80 kg and 25 g : 625 g form a proportion ?
Solution:

Question 9.
10 kg sugar cost ₹ 350. If x kg sugar of the same kind costs ₹ 175, find the value of x
Solution:

Question 10.
The length of two ropes are in the ratio 7 : 5. Find the length of:
(i) shorter rope, if the longer one is 22.5 ni
(ii) longer rope, if the shorter is 9.8 m.
Solution:

Question 11.
If 4, x and 9 are in continued proportion, find the value of x.
Solution:

Question 12.
If 25, 35 and x are in continued proportion, find the value of x.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions