NCERT solution class 8 chapter 8 Comparing quantities

Exercise 8.1  Exercise 8.2  Exercise 8.3

Exercise 8.2

Question 1

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

Sol :

Let the original salary be x. It is given that the new salary is Rs 1,54,000.

Original salary + Increment = New salary

However, it is given that the increment is 10% of the original salary.

Therefore,

Thus, the original salary was Rs 1,40,000.

 

Question 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?

Sol :

It is given that on Sunday, 845 people went to the zoo and on Monday, 169 people went.

Decrease in the number of people = 845 − 169 = 676

Percentage decrease =

 

Question 3

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

Sol :

It is given that the shopkeeper buys 80 articles for Rs 2,400.

Cost of one article =

Profit percent = 16

Selling price of one article = C.P. + Profit = Rs (30 + 4.80) = Rs 34.80

 

Question 4

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

Sol :

Total cost of an article = Cost + Overhead expenses

= Rs 15500 + Rs 450

= Rs 15950

∴Selling price of the article = C.P. + Profit = Rs (15950 + 2392.50)

= Rs 18342.50

 

Question 5

A VCR and TV were bought for Rs 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.

Sol :

C.P. of a VCR = Rs 8000

The shopkeeper made a loss of 4 % on VCR.

This means if C.P. is Rs 100, then S.P. is Rs 96.

When C.P. is Rs 8000, S.P. = = Rs 7680

C.P. of a TV = Rs 8000

The shopkeeper made a profit of 8 % on TV.

This means that if C.P. is Rs 100, then S.P. is Rs 108.

When C.P. is Rs 8000, S.P. = = Rs 8640

Total S.P. = Rs 7680 + Rs 8640 = Rs 16320

Total C.P. = Rs 8000 + Rs 8000 = Rs 16000

Since total S.P.> total C.P., there was a profit.

Profit = Rs 16320 − Rs 16000 = Rs 320

Therefore, the shopkeeper had a gain of 2% on the whole transaction.

 

Question 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 Rs 1450 and two shirts marked at Rs 850 each?

Sol :

Total marked price = Rs (1,450 + 2 × 850) = Rs (1,450 +1,700) = Rs 3,150

Given that, discount % = 10%

Discount =

Also, Discount = Marked price − Sale price

Rs 315 = Rs 3150 − Sale price

∴ Sale price = Rs (3150 − 315) = Rs 2835

Thus, the customer will have to pay Rs 2,835.

 

Question 7

A milkman sold two of his buffaloes for Rs 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)

Sol :

S.P. of each buffalo = Rs 20000

The milkman made a gain of 5% while selling one buffalo.

This means if C.P. is Rs 100, then S.P. is Rs 105.

C.P. of one buffalo = = Rs 19,047.62

Also, the second buffalo was sold at a loss of 10%.

This means if C.P. is Rs 100, then S.P. is Rs 90.

∴C.P. of other buffalo = = Rs 22222.22

Total C.P. = Rs 19047.62 + Rs 22222.22 = Rs 41269.84

Total S.P. = Rs 20000 + Rs 20000 = Rs 40000

Loss = Rs 41269.84 − Rs 40000 = Rs 1269.84

Thus, the overall loss of milkman was Rs 1,269.84.

 

Question 8

The price of a TV is Rs 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,

Sol :

On Rs 100, the tax to be paid = Rs 12

On Rs 13000, the tax to be paid will be

= Rs 1560

Required amount = Cost + Sales Tax = Rs 13000 + Rs 1560

= Rs 14560

Thus, Vinod will have to pay Rs 14,560 for the T.V.

 

Question 9

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

Sol :

Let the marked price be x.

Also,

Discount = Marked price − Sale price

Thus, the marked price was Rs 2000.

Question 10

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

Sol :

The price includes VAT.

Thus, 8% VAT means that if the price without VAT is Rs 100, then price including VAT will be Rs 108.

When price including VAT is Rs 108, original price = Rs 100

Thus, the price of the hair-dryer before the addition of VAT was Rs 5,000.

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