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Class 8 NCERT Solutions – Chapter 8 Comparing Quantities – Exercise 8.2
  • Last Updated : 20 Nov, 2020

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

Solution:

Let the initial salary was 100.

He got 10 % increment so increased salary is 110.

Increased salary(110%) is equal to 154000

Base salary(100%) is equal to 154000 ×  (100 / 110) = 140000



Hence his original salary was 140000.

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?

Solution:

Given that On Sunday 845 people went to the Zoo.

On Monday only 169 people went.

Decrease in people = 845 – 169 = 676 

Percentage  decrease = (decrease / initial quantity) 100

                                  = (676 / 845) × 100

                                  = (0.8) × 100



                                  = 80%

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

Question 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:

A shopkeeper buys 80 articles for 2,400

Cost price of one article is 2400 / 80 = 30

Percentage Profit  = 16

Profit  = (C.P. ×  Percentage Profit) / 100 

Profit = (30 × 16) / 100

Profit = 4.8

Selling price of one article = C.P. + Profit

                                         = (30 + 4.80)

                                         = 34.80

Hence the selling price of one article is 34.80.

Question 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:

Total cost of an article after repair  = Cost + repair expenses

                                                       = 15500 + 450

                                                       = 15950 rupees 

Profit percent = 15

Profit = (C.P. ×  Percentage Profit) / 100 

Profit = (15950 × 15) / 100 = 2392.50



 Selling price of the article = C.P. + Profit

                                         = (15950 + 2392.50)

                                         =  18342.50

Hence  the selling price of the article is 18342.50 

Question 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:

C.P. of a VCR = 8000

C.P. of a TV = 8000 

As the cost price of both the article are same so profit and loss calculated on same  cost price would be same

so effective profit / loss =  (8% profit  – 4% loss)

                                     = 4% profit

So gain = C.P.  (profit  / 100)

             = 8000 (4 / 100)

             = 320

Hence the gain percent on the whole transaction is 320.

Profit % on the whole transaction = (Profit / Total CP) x 100

                                                     = (320 / 16000) x 100

                                                     = 2%

Question 6. During a sale, a shop offered a discount of 10% on the market 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:

As the discount is offered on all the article by the shopkeeper so discount can be calculated from total marked price.

 So Total marked price = (1,450 + 2 × 850)

                                    = (1,450 + 1,700)

                                    = 3,150

Given that, discount percentage = 10%

Discount = (3150 ×10 ) / 100 = 315

Also,  Sale price = Marked price – Discount

 Sale price =  (3150 − 315)

                 =  2835 

Hence  the customer will have to pay  2,835. 

Question 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)

Solution:

Let us consider C.P. of buffaloes are 100 each

On one he made a gain of 5%

 if C.P. is 100 Then S.P.= 105

So cost price = (C.P. / S.P.) 20000

                   = (100 / 105) 20000

                   = 19,047.62       

on the other a loss of 10 %

 if C.P. is 100  Then S.P. = 90

∴ C.P. of other buffalo = (100 / 90) × 20000

                                    = 22222.22 

Total C.P. = 19047.62 + 22222.22 

                =  41269.84

Total S.P. = 20000 + 20000 = 40000

Loss = 41269.84 − 40000 = 1269.84

So the overall loss of milkman was 1269.84

Question 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.

Solution:

Let C.P. is 100

 the tax to be paid = 12

The tax to be paid will be on 13000 = (12 / 100) × 13000

                                                         = 1560

Required amount to pay = Cost + Sales Tax

                                       = 13000 + 1560

                                       = 14560

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

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

Solution:

Let the marked price of the article is 100

Discount given = 20

S.P. = (100 – 20) = 80

when assumed S.P. is 80 actual S.P.is 1600 

then marked price 100 is =1600 × (100 / 80)

                                        = 2000

Hence  the marked price was 2000.

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

Solution:

Let the original price is 100

then price including VAT will be 108.

When price including VAT is 108

Then original price = 100

When price including VAT is 5400, original price = (100 / 108) × 5400

                                                                            = 5000

Hence the price of the hair-dryer before the addition of VAT was 5000.

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

Solution:

Let the original price of article excluding GST was 100

After including GST purchased price will be 118

So 118% ( including GST ) = 1239

100% ( excluding GST ) = 1239 × (100 / 118)

                                     = 1050

Hence  the price of the article before GST was added was 1050.

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