SChand Composite Mathematics Class 7 Chapter 2 Fractions Exercise 2C

 Exercise 2C

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Q1 | Ex-2C |Class 8 | Fractions |S.Chand | Composite Mathematics | Chapter 2 | myhelper

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Question 1

$\frac{3}{5}$ of a road is to be resurfaced. If the road is $2 \frac{3}{5} \mathrm{~km}$ long, what length in kilometres is to be resurfaced?

Sol :

$=\frac{3}{5} \times 2 \frac{3}{5}$

$=\frac{3}{5} \times \frac{2 \times 5+3}{5}=\frac{3}{5} \times \frac{13}{5}$

$=\frac{39}{25}=1\frac{14}{25}$

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Question 2

You spent $1 \frac{1}{2}$ hours on homework last night and $\frac{1}{4}$ of that time was spent on mathematics. What fraction of hour did you spent on math's?

Sol :

$=\frac{1}{4} \text{ of } \frac{3}{2}$

$=\frac{1}{4} \times \frac{3}{2}=\frac{3}{8}$ hour

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Question 3

Cost of 1 litre Petrol is $₹ 42 \frac{4}{7}$. What is the cast of $10 \frac{1}{2}$ litres petrol?

Sol :

$=₹ 42 \frac{4}{7}=\frac{42 \times 7+4}{7}$

$=\frac{298}{7} \times \frac{21}{2}$

=149×3=447

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Question 4

After covering $\frac{3}{4}$ of my Journey, I find that 15 km is still left. How much distance in the total journey?

Sol :

Let the total journey be x.

Journey covered$=\frac{3}{4}$ of total journey is $\frac{3x}{4}$

A.T.Q

Total journey-Journey covered=15 km

$x-\frac{3x}{4}=15$

$\frac{4x-3x}{4}=15$

$\frac{x}{4}=15$

x=15×4=60 km

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Question 5

In a school, $\frac{4}{9}$ of the students are boys and the number of girls is 775 . Find the number of boys in the school.

Sol :

Let the total students be x.

Number of boys$=\frac{4}{9} \text{ of } x=\frac{4x}{9}$

Number of girls = 775

Total students=Number of boys + Number of girls

$x=\frac{4x}{9}+775$

$x-\frac{4x}{9}=775$

$frac{9x-4x}{9}=775$

5x=775×9

$x=\frac{6975}{5}$

Total students=x=1395

Number of boys$=\frac{4}{9} \text{ of } 1395=\frac{4}{9} \times 1395$

=620

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Question 6

A tank is $\frac{3}{5}$ full of water. 50 litres more are required to fill it up. How many litres can the tank hold?

Sol :

Let the tank hold x litres of water.

Tank is filled= $\frac{3}{5}$ of x $=\frac{3x}{5}$

A.T.Q

Tank filled+50 litres=Total 

$\frac{3x}{5}+50=x$

$x-\frac{3x}{5}=50$

$\frac{5x-3x}{5}=50$

2x=50×5

$x=\frac{250}{2}=125$ litres

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Question 7

A Sum of money was divided between Rajeev and Ashish on so that Rajeev gets $\frac{7}{19}$ of the whole amount. If he gets 5600 , how much was the total sum.

Sol :

Let the total money be x

Rajeev receives$=\frac{7}{19}$ of total$=\frac{7x}{19}$

Also,$\frac{7x}{19}=5600$

7x=5600×19

$x=\frac{5600 \times 19}{7}$

Total money=x=15200

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Question 8

Mr Joshi bequeath $\frac{1}{3}$ of his money to his son, $\frac{1}{5}$ to his daughter and the remaining to his wife who got 42000. What was the total amount?

Sol :

Total money be x

Also, Total money=Money received by son + Money received by daughter + Money received by wife

x=$\frac{1}{3}$ of x + $\frac{1}{5}$ of x + 42000

$x=\frac{1x}{3}+\frac{1x}{5}+42000$

$x-\frac{1x}{3}-\frac{1x}{5}=42000$

$\frac{15x-5x-3x}{15}=42000$

7x=42000×15

$x=\frac{42000 \times 15}{7}$

Total money=x=6000×15=90000

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Question 9

A boy spends $\frac{3}{4}$ of his pocket money and then $\frac{4}{5}$ of the remainder is given to his sister. If he has 40 left , what did he have at first?

Sol :

Total pocket money be x.

Boy spends$=\frac{3}{4}$ of x$=\frac{3x}{4}$

Remaining=$x-\frac{3x}{4}=\frac{4x-3x}{4}=\frac{x}{4}$

Sister receives$\frac{4}{5}$ of remaining $=\frac{4}{5} \times \frac{x}{4}=\frac{x}{5}$

Remaining - Sister received amount=40

$\frac{x}{4}-\frac{x}{5}=40$

$\frac{5x-4x}{20}=40$

$\frac{x}{20}=40$

Total pocket money be x=40×20=800

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Question 10

A magazine has 60 Pages of which $\frac{7}{12}$ are for ad. , $\frac{4}{15}$ have only photographs on them and the rest are for articles and stories. How many pages have articles and stories on them?

Sol :

Total pages=Pages for ads+ Photographs + Articles and stories

60=$\frac{7}{12}$ of 60+$\frac{4}{15}$ of 60 + x

$60=\frac{7}{12} \times 60+ \frac{4}{15} \times 60$ +x

60=7×5+4×4+x

60=35+16+x

60=51+x

x=60-51=9 pages for Articles and stories

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Question 11

Steve is planning to take 3 loaves of bread. Each loaf cost for $5\frac{1}{4}$ cups of flour. He knows he has 20 cups on hand . Will he have enough flour left for a cake recipe that requires $3 \frac{5}{4}$ cups?

Sol :

Loaf cost $5\frac{1}{4}=\frac{5 \times 4+1}{4}=\frac{21}{4}$ cups of flour

To make 3 loaves of bread it requires $=3 \times \frac{21}{4}=\frac{63}{4}$

Steve has 20 cups, so what is left is:

$20-\frac{63}{4}=\frac{20 \times 4-63}{4}=\frac{80-63}{4}=\frac{17}{4}$

Cake recipe that requires $\frac{3 \times 4+5}{4}=\frac{17}{4}$

Answer is yes.