# Comparing Quantities

## Exercise 8.3

**Question 1:** Tell what is the profit or loss in the following transactions. Also find profit per cent or loss per cent in each case.

(a) Gardening shears bought for Rs. 250 and sold for Rs. 325.

**Answer:** Cost Price = Rs. 250 and Selling Price = Rs. 325

Profit = SP – CP

`= 325 – 250 = Rs. 75`

Percentage profit:

`=(text(Profit)xx100)/(CP)`

`=(75xx100)/(250)=30%`

(b) A refrigerator bought for Rs. 12,000 and sold at Rs. 13,500.

**Answer:** CP = Rs. 12000 and SP = Rs. 13500

Profit = SP – CP `= 13500 – 12000 = Rs. 1500`

Percentage profit: `=(text(Profit)xx100)/(CP)`

`=(1500xx100)/(12000)=12.5%`

(c) A cupboard bought for Rs. 2,500 and sold at Rs. 3,000.

**Answer:** CP = 2500 and SP = 3000

Profit = SP – CP `= 3000 – 2500 = Rs. 500`

Percentage profit: `=(text(Profit)xx100)/(CP)`

`=(500xx100)/(2500)=20%`

(d) A skirt bought for Rs. 250 and sold at Rs. 150.

**Answer:** CP = Rs. 250 and SP = Rs. 150

Profit = SP – CP `= 150 – 250 = - 100`

Negative sign shows it is a loss.

Percentage loss: `=(text(Loss)xx100)/(CP)`

`=(100xx100)/(250)=40%`

**Question 2:** Convert each part of the ratio to percentage:

(a) 3:1

**Answer:** Total `= 3 + 1 = 4`

Percentage of first part: `=3/4xx100=75%`

Percentage of second part: `=1/4xx100=25%`

(b) 2:3:5

**Answer:** Total `= 2 + 3 + 5 = 10`

Percentage of first part: `=(2)/(10)xx100=20%`

Percentage of second part: `=(3)/(10)xx100=30%`

Percentage of third part: `=(5)/(10)xx100=50%`

(c) 1:4

**Answer:** Total `= 1 + 4 = 5`

Percentage of first part: `=1/5xx100=20%`

Percentage of second part: `=4/5xx100=80%`

(d) 1: 2:5

**Answer:** Total `= 1 + 2 + 5 = 8`

Percentage of first part: `=1/8xx100=12.5%`

Percentage of second part: `=2/8xx100=25%`

Percentage of third part: `=5/8xx100=62.5%`

**Question 3:** The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.

**Answer:** Initial population = 25000 and final population = 24500

Decrease in population `= 25000 – 24500 = 500`

Percentage decrease:

`=(text(Decrease)xx100)/text(Initial Population)`

`=(500xx100)/(25000)=2%`

**Question 4:** Arun bought a car for Rs. 3,50,000. The next year, the price went upto Rs. 3,70,000. What was the Percentage of price increase?

**Answer:** Initial price = Rs. 350000 and final price = 370000

Increase `= 370000 – 350000 = Rs. 20000`

Percentage increase:

`=(text(Increase)xx100)text(Initial Price)`

`=(20000xx100)/(350000)=(200)/(35)`

`=(40)/(7)=5\5/7%`

**Question 5:** I buy a T.V. for Rs. 10,000 and sell it at a profit of 20%. How much money do I get for it?

**Answer:** CP = Rs. 10000 and percentage profit = 20%

Profit = CP `xx` Percentage Profit

`=10000xx(20)/(100)=2000`

SP = CP + Profit `= 10000 + 2000 = Rs. 12000`

**Question 6:** Juhi sells a washing machine for Rs. 13,500. She loses 20% in the bargain. What was the price at which she bought it?

**Answer:** SP = Rs. 13500 and percentage loss = 20%

CP can be calculated as follows:

`CP=(SP\xx100)/(100-%text(Loss)`

`=(13500xx100)/(80)=Rs. 16875`

**Alternate Method:** Let us assume that CP = 100 then loss = 20

In this case, SP = CP – Loss `= 100 – 20 = 80`

When SP is 80 then CP is 100.

Hence, when SP is 1 then CP is `(100)/(80)`

Hence, when SP is 13500 then CP is

`=(13500xx100)/(80)=Rs. 16875`

**Question 7:** (i) Chalk contains calcium, carbon and oxygen in the ratio 10:3:12. Find the percentage of carbon in chalk. (ii) If in a stick of chalk, carbon is 3g, what is the weight of the chalk stick?

**Answer:** Total `= 10 + 3 + 12 = 25`

Percentage of carbon:

`=(3)/(25)xx100=12%`

Since ratio of carbon and weight of carbon are same, i.e. 3

Hence, weight of chalk stick = total of ratios = 25 g

**Question 8:** Amina buys a book for Rs. 275 and sells it at a loss of 15%. How much does she sell it for?

**Answer:** CP = Rs. 275 and loss = 15%

Loss:

`=275xx(15)/(100)=Rs. 41.25`

SP = CP – Loss `= 275 – 41.25 = Rs. 233.75`

**Question 9:** Find the amount to be paid at the end of 3 years in each case:

(a) Principal = Rs. 1,200 at 12% p.a.

**Answer:** P = Rs. 1200, r = 12% and t = 3 years

Simple Interest `=(P\xx\r\xx\t)/(100)`

`=(1200xx12xx3)/(100)=Rs. 432`

Amount = Principal + Interest `= 1200 + 432 = Rs. 1632`

(b) Principal = Rs. 7,500 at 5% p.a.

**Answer:** P = Rs. 6500, r = 5% and t = 3 years

Simple Interest `=(P\xx\r\xx\t)/(100)`

`=(7500xx5xx3)/(100)=Rs. 1125`

Amount = Principal + Interest `= 7500 + 1125 = Rs. 8625`

**Question 10:** What rate gives Rs. 280 as interest on a sum of Rs. 56,000 in 2 years?

**Answer:** P = Rs. 56000, SI = Rs. 280, t = 2 years and r = ?

`r=(SI\xx100)/(P\xx\t)`

`=(280xx100)/(56000xx2)=1/4%`

**Question 11:** If Meena gives an interest of Rs. 45 for one year at 9% rate p.a. What is the sum she has borrowed?

**Answer:** SI = Rs. 45, t = 1 year, r = 9% and P = ?

`P=(SI\xx100)/(r\xx\t)`

`=(45xx100)/(9xx1)=Rs. 500`