Class 8th mathematics Comparing Quantities chapter 8 all exercises solution

 EXERCISE 8.1 

1. Find the ratio of the following.
(a) Speed of a cycle 15 km per hour to the speed of scooter 30 km per hour.
(b) 5 m to 10 km
(c) 50 paisa to ₹5 

Solution -

(a) 

Speed of a cycle : the speed of scooter 

15 km per hour : 30 km per hour.

1530=12

Means 1 : 2

Hence, the ratio of the Speed of a cycle 15 km per hour and the speed of scooter 30 km per hour is 1 : 2.

(b) 

5 m : 10 km

5 m : 10 × 1000 m (1km = 1000 m)

5 : 10000

1 : 2000

Hence, the ratio of 5 m and 10 km is 1 : 2000.

(c) 

50 paise : ₹5 

50 paisa : 500 paisa (₹1 = 100 paisa)

1 : 10

Hence, the ratio of 50 paise and ₹5 is 1 : 10.

2. Convert the following ratios to percentages. 
(a) 3 : 4 (b) 2 : 3 

Solution -

(a) 3 : 4 

We know that the ratio is written as in the form of fraction. After written in fraction multiply by 100.

34×100=75 %

(b) 2 : 3 

We know that the ratio is written as in the form of fraction. After written in fraction multiply by 100.

23×100=66.67 %

3. 72% of 25 students are interested in mathematics. How many are not interested in mathematics? 

Solution- 

According to the question,

Total student = 25 

From 100%, 72% students interested in mathematics.

100% - 72% = 28% students are not interested in mathematics.

And 

100% = 25 student

1% = 14 students

28 × 1% = 28 × 14 students

28% = 7 students

Hence,  7 students are not interested in mathematics.

4. A football team won 10 matches out of the total number of matches they played. If their win percentage was 40, then how many matches did they play in all? 

Solution - According to the question,

Total number of matches won = 10

The win percentage is = 40%

Let, 

Total number of matches they played = x

Then, 

10x=40100⇒x=1040×100

 x=100×10/40=25

Hence, 25 matches did they play in all.

10x=40100⇒x=1040×100

5. If Chameli had ₹600 left after spending 75% of her money, how much did she have in the beginning? 

Solution-  According to the question,

Total money she spend = 75%

She have Total money in the beginning = 100%

Money left after spending = ₹600

Money left after spending in percentage = 100% - 75% = 25%

Then,

25% = ₹600

1% =  ₹24

100% = ₹2400

Hence, she have ₹2400in the beginning.

6. If 60% people in a city like cricket, 30% like football and the remaining like other games, then what per cent of the people like other games? If the total number of people is 50 lakh, find the exact number who like each type of game.

Solution- 

Total number of people = 50,00,000

Number of people who like cricket = 60% of 50,00,000
= 60100 × 50,00,000 = 30,00,000

Number of people who like football = 30% of 50,00,000
= 30100 × 50,00,000 = 15,00,000

Number of people who like other games = 50,00,000 – (30,00,000 + 15,00,000) = 50,00,000 – 45,00,000 = 5,00,000

Percentage of the people who like other games = 5000005000000 × 100 = 10% 

Hence, 10% of people like other game.

EXERCISE 8.2 

1. A man got a 10% increase in his salary. If his new salary is ` 1,54,000, find his original salary. 

Solution -

According to the question,

Let the original salary = x

new salary =x+x×10%% 

Given,  x+x×10%=₹1,54,000

Then,

x+x×10%  = ₹ 1,54,000

x+x×10100=₹1,54,000

110100x=₹1,54,000

x=₹1,54,000×100110

x=₹1,40,000

Hence, his original salary is 1,40,000.

2. On Sunday 845 people went to the Zoo. On Monday only 169 people went. What is the per cent decrease in the people visiting the Zoo on Monday? 

Solution- According to the question,

On Sunday people went to the Zoo = 845 

On Monday only people went to the Zoo = 169 

Then, 

On Monday 845 - 169 = 676 less people went to the zoo.

The per cent is decrease in the people visiting the Zoo on Monday

=676845×100=80%

Hence, 80%  is decrease in the people visiting the Zoo on Monday.

3. A shopkeeper buys 80 articles for `₹2,400 and sells them for a profit of 16%. Find the selling price of one article. 

Solution-  According to the question,

A shopkeeper buys 80 articles for `₹2400

Means One article buy for ₹30

sells them for a profit is 16% in one article also

16% of ₹30 

=16100×₹30=₹4.8 

new article price is ₹30 + ₹4.8 = ₹34.8

Hence, the selling price of one article is ₹34.8.

4. The cost of an article was `₹15,500. `₹450 were spent on its repairs. If it is sold for a profit of 15%, find the selling price of the article. 

Solution- According to the question,

Total cost of an article = the cost of article + spent on its repairs

Total cost of an article = ₹15,500 + ₹450 = ₹15,950

Article is sold for a profit of 15% on ₹15,950.

Then,

profit  

=15100×₹15950=₹2392.5

Profit = ₹2392.5

As we know,

Selling price = Cost price + profit

Selling price = ₹15,950 + ₹2392.5 = ₹18342.5

Hence, the seling price of the article is  ₹18342.5.

5. A VCR and TV were bought for `₹8,000 each. The shopkeeper made a loss of 4% on the VCR and a profit of 8% on the TV. Find the gain or loss percent on the whole transaction. 

Solution- According to the question,

A VCR and TV were bought for `₹8,000

The shopkeeper made a loss of 4% on the VCR.

4% of 8000,

 =4100×₹8000=₹320

On VCR made ₹320 loss

The shopkeeper made a profit of 8% on the TV.

8% of 8000,

 =8100×₹8000=₹640

On TV made ₹640 Profit.

The gain or loss on the whole transaction,

₹640 - ₹320 = ₹320 

₹320 gain on the whole transaction,

The gain or loss percent on the whole transaction,

Total cost of both VCR and TV is  ₹16000

Then,

Gain percent 

=₹320₹16000×100=2%

  Hence, The gain percent on the whole transaction is 2%.

6. During a sale, a shop offered a discount of 10% on the marked prices of all the items. What would a customer have to pay for a pair of jeans marked at `₹1450 and two shirts marked at `₹850 each? 

Solution-

Discount = 10% 

Customer buy a pair of jeans + two shirts at ₹1450 + ₹850 = ₹2300

Total discount is,

 =10100×₹2300=₹230

A customer pay =  ₹2300 -  ₹230 = ₹2070

Hence, a customer would have to pay ₹2070 for a pair of jeans marked at `₹1450 and two shirts marked at `₹850 each. 

7. A milkman sold two of his buffaloes for `₹20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss. (Hint: Find CP of each)

8. The price of a TV is `₹13,000. The sales tax charged on it is at the rate of 12%. Find the amount that Vinod will have to pay if he buys it. 

9. Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is `₹1,600, find the marked price. 

10. I purchased a hair-dryer for ` 5,400 including 8% VAT. Find the price before VAT was added. 

11. An article was purchased for `₹1239 including GST of 18%. Find the price of the article before GST was added?