5 Marks Questions

Question 15 Marks

Convert each part of the ratio to percentage
(i) 3 : 1
(ii) 2 : 3 : 5
(iii) 1 : 4
(iv) 1 : 2 : 5

Answer

(i) Given, ratio = 3:1
Sum of the parts=3+1=4
$\therefore$ Percentage of first part $=\left(\frac{3}{4} \times 100\right) \%=75 \%$
and percentage of second part $=\left(\frac{1}{4} \times 100\right) \%=25 \%$
(ii) Given, ratio = 2:3:5
Sum of the parts = 2 + 3 + 5 = 10
$\therefore$ Percentage of first part $=\left(\frac{2}{10} \times 100\right) \%$
$=(2 \times 10) \%=20 \%$
Percentage of second part $=\left(\frac{3}{10} \times 100\right) \%$
$=(3 \times 10) \%=30 \%$
and percentage of third part $=\left(\frac{5}{10} \times 100\right) \%$
$=(5 \times 10) \%=50 \%$
(iii) Given, ratio = 1:4; Sum of the parts =1+4=5
$\therefore$ Percentage of first part $=\left(\frac{1}{5} \times 100\right) \%=20 \%$
and percentage of second part $=\left(\frac{4}{5} \times 100\right) \%$
$=(4 \times 20) \%=80 \%$
(iv) Given, ratio=1:2:5
Sum of the parts = 1 + 2 + 5 = 8
$\therefore$ Percentage of first part $=\left(\frac{1}{8} \times 100\right) \%=\frac{25}{2} \%$
$=12.5 \%$
Percentage of second part $=\left(\frac{2}{8} \times 100\right) \%$
$=\left(\frac{100}{4}\right) \%=25 \%$
and percentage of third part $=\left(\frac{5}{8} \times 100\right) \%$
$=\left(\frac{125}{2}\right) \%=62.5 \%$

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Question 25 Marks

Tell what is the profit or loss in the following transactions. Also, find profit per cent or loss per cent in each case.
(i) Gardening shears bought for ₹ 250 and sold for ₹ 325.
(ii) A refrigerator bought for ₹ 12000 and sold at ₹ 13500.
(iii) A cupboard bought for ₹ 2500 and sold at ₹ 3000.
(iv) A skirt bought for ₹ 250 and sold at ₹ 150.

Answer

(i) Given, CP of gardening shears $=$ ₹ $250$
SP of gardening shears $=$ ₹ $325$
Since, $CP < SP$, then
Profit $= SP - CP =$ ₹ $(325-250)=$ ₹ $75$
So, profit $\%=\left(\frac{\text { Profit }}{ CP } \times 100\right) \%=\left(\frac{75}{250} \times 100\right) \%$
$=(3 \times 10) \%=30 \%$
(ii) Given, CP of a refrigerater $=$ ₹ $12000$
SP of a refrigerater $=$ ₹ $13500$
Since, CP $<$ SP, then
Profit $=S P-C P=$ ₹ $(13500-12000)=$ ₹ $1500$
So, profit $\%=\left(\frac{\text { Profit }}{ CP } \times 100\right) \%=\left(\frac{1500}{12000} \times 100\right) \%$
$=\frac{150}{12} \%=12.5 \%$
(iii) Given, CP of a cupboard $=$ ₹ $2500$
SP of a cupboard $=$ ₹ $3000$
Since, CP $<$ SP, then
Profit $=S P-C P=$ ₹ $(3000-2500)=$ ₹ $500$
So, profit $\%=\left(\frac{\text { Profit }}{ CP } \times 100\right) \%$
$=\left(\frac{500}{2500} \times 100\right) \%$
$=\frac{500}{25} \%=20 \%$
(iv) Given, CP of a skirt $=$ ₹ $250$
SP of a skirt $=$ ₹ $150$
Since, $C P>S P$, then
Loss $= CP - SP =$ ₹ $(250-150)=$ ₹ $100$
So, loss $\%=\left(\frac{\text { Loss }}{ CP } \times 100\right) \%=\left(\frac{100}{250} \times 100\right) \%$
$=(4 \times 10) \%=40 \%$

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Question 35 Marks

Find the whole quantity, If
(i) 5% of it is 600
(ii) 12% of it is ₹ 1080
(iii) 40% of it is 500 km
(iv) 70% of it is 14 minutes
(v) 8% of it is 40 litres

Answer

(i) Let the whole quantity be x.
$\begin{array}{l}\therefore 5 \% \text { of } x=600 \Rightarrow \frac{5}{100} \times x=600 \\ \Rightarrow x=\frac{600 \times 100}{5}=600 \times 20=12000\end{array}$
Hence, the whole quantity is 12000.
(ii) Let the whole quantity be ₹ x.
$\therefore 12 \% \text {of} x=$ ₹ $1080 $
$\Rightarrow \frac{12}{100} \times x=1080 $
$\Rightarrow x=\frac{1080 \times 100}{12}=90 \times 100=9000$
Hence, the whole quantity is ₹ 9000.
(iii) Let the whole quantity be x km.
$\begin{array}{l}\therefore 40 \% \text { of } x=500 km \Rightarrow \frac{40}{100} \times x=500 \\ \Rightarrow x=\frac{500 \times 100}{40}=50 \times 25=1250 km\end{array}$
Hence, the whole quantity is 1250 km.
(iv) Let the whole quantity be x minutes.
$\begin{array}{l}\therefore 70 \% \text { of } x=14 \text { minutes } \\ \Rightarrow \frac{70}{100} \times x=14\end{array}$
$\begin{aligned} \Rightarrow x & =\frac{14 \times 100}{70} \text { minutes } \\ & =2 \times 10 \text { minutes }=20 \text { minutes }\end{aligned}$
Hence, the whole quantity is 20 minutes.
(v) Let the whole quantity be x litres.
$\therefore 8 \%$ of $x=40$ litres $\Rightarrow \frac{8}{100} \times x=40$
$\Rightarrow x=\frac{40 \times 100}{8}=5 \times 100=500$ litres
Hence, the whole quantity is 500 litres.

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