Mathematics – Class 8 – Chapter 8 – Comparing Quantities – Exercise 8.2 – NCERT Exercise Solution

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

Solution:

Let us assume the original salary be x

Given, the new salary is ₹1,54,000

So,

Original salary + Increment = New salary

Given, the increment is 10% of the original salary

Now,

(x + 10/100 × x) = 154000

x + x/10 = 154000

11x/10 = 154000

x = 154000 × 10/11

= 140000

Hence, the original salary was ₹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:

Given,

Total number of people went to zoo on Sunday = 845

Total number of people went to zoo on Monday = 169

So,

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

Thus,

Percentage decrease = (Decrease in the number of people/Number of people who went to zoo on Sunday) x 100%

= (676/845 x 100)%

= 80%

Hence, required percentage is 80%.

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:

Given, the shopkeeper buys 80 articles of ₹ 2,400

Cost of one article = 2400/80 = ₹ 30

Given, profit percentage = 16%

Now,

Profit percentage = Profit/C.P x 100

16 = Profit/30 x 100

Profit = (16 x 30)/100

= ₹ 4.8

Hence, selling price of one article = C.P + Profit

= ₹ (30 + 4.80)

= ₹ 34.80

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:

Given,

cost of an article = ₹ 15,500

Repairing cost = ₹ 450

Profit percent = 15%

Now,

Total cost of an article = Cost + Overhead expenses

= ₹15500 + ₹450

= ₹15950

Profit percentage = 15%

Profit percentage = Profit/C.P x 100

15 = Profit/15950 x 100

Profit = (15 x 15950)/100

= 2392.50

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

= ₹(15950 + 2392.50)

= ₹18342.50

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:

Given,

Cost Price (CP) of a VCR = ₹ 8000

The shopkeeper made a loss of 4 % on VCR

So,

This means if Cost Price is ₹ 100, then Selling Price (SP) is ₹ 96.

Now, When Cost Price is ₹ 8000

Selling Price = (96/100 x 8000) = ₹ 7680

Cost Price of a TV = ₹ 8000

Given, the shopkeeper made a profit of 8 % on TV.

This means that if Cost Price is ₹ 100, then Selling Price is ₹ 108.

When Cost Price is ₹ 8000,

Selling Price = (108/100 x 8000) = ₹ 8640

Total Selling Price = ₹ 7680 + ₹ 8640 = ₹ 16320

Total Cost Price = ₹ 8000 + ₹ 8000 = ₹ 16000

Since, total Selling Price total Cost Price ⇒ profit

Profit = ₹ 16320 − ₹ 16000 = ₹ 320

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

= 320/16000 x 100

= 2%

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

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:

Marked price on jeans = ₹ 1450

Marked price of one shirt = ₹ 850

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

= ₹ (1,450 +1,700)

= ₹ 3,150

Given, discount percentage = 10%

Discount = ₹ (10/100 x 3150) = ₹ 315

Also, Discount = Marked price − Sale price

₹ 315 = ₹ 3150 − Sale price

So, Sale price = ₹ (3150 − 315)

= ₹ 2835

Hence, the customer will have to pay ₹ 2,835.

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:

Selling Price (SP)

Cost Price (CP)

S.P. of one buffalo = ₹ 20,000

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

So, it means if C.P. is ₹ 100, then S.P. is ₹ 105.

C.P. of one buffalo = 100/105 × 20000

= ₹ 19,047.62

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

So, it means if C.P. is ₹ 100, then S.P. is ₹ 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

Hence, the overall loss of milkman was ₹ 1,269.84

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:

Price of TV = ₹ 13,000

On ₹ 100, the tax to be paid = ₹ 12

Now, on ₹ 13000, the tax to be paid will be = 12/100 × 13000

= ₹ 1560

So, the required amount = Cost + Sales Tax

= ₹ 13000 + ₹ 1560

= ₹ 14560

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

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.

Solution:

Let us assume the marked price be x

Given discount = 20%

Discount percent = Discount/Marked Price x 100

20 = Discount/x × 100

Discount = 20/100 × x

= x/5

Also,

Discount = Marked price – Sale price

x/5 = x – ₹ 1600

x – x/5 = 1600

4x/5 = 1600

x = 1600 x 5/4

= 2000

Hence, the marked price was ₹ 2000.

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

Solution:

Price of hair-dryer = ₹ 5,400

VAT percent = 8%

So, 8% VAT means that,

 If the price without VAT is ₹ 100,

Then, price including VAT will be ₹ 108

Now,

When price including VAT is ₹ 108,

Then, original price = ₹ 100

When price including VAT is ₹ 5400,

Then, original price = ₹ (100/108 × 5400)

= ₹ 5000

Hence, the price of the hair-dryer before the addition of VAT was ₹ 5,000.

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