Exercise 2C
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 :
$=\frac{3}{5} \times 2 \frac{3}{5}$
$=\frac{3}{5} \times \frac{2 \times 5+3}{5}=\frac{3}{5} \times \frac{13}{5}$
$=\frac{39}{25}=1\frac{14}{25}$
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
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
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
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
5x=775×9
$x=\frac{6975}{5}$
Total students=x=1395
Number of boys$=\frac{4}{9} \text{ of } 1395=\frac{4}{9} \times 1395$
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
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
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
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
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
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.
No comments:
Post a Comment