### Comparing Quantities - Solutions 2

CBSE Class –VIII Mathematics

NCERT Solutions

CHAPTER - 8

Comparing Quantities (Ex. 8.2)

NCERT Solutions

CHAPTER - 8

Comparing Quantities (Ex. 8.2)

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

Ans. Let original salary be Rs.100.

Therefore New salary i.e., 10% increase

= 100 + 10 = Rs.110

New salary is Rs.110, when original salary = Rs.100

New salary is Rs.1, when original salary =

New salary is Rs.1,54,000, when original salary = = Rs.1,40,000

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

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

Ans. On Sunday, people went to the Zoo = 845

On Monday, people went to the Zoo = 169

Number of decrease in the people = 845 – 169 = 676

Decrease percent = = 80%

Hence decrease in the people visiting the Zoo is 80%.

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.

Ans. No. of articles = 80

Cost Price of articles = Rs. 2,400

And Profit = 16%

Cost price of articles is Rs.100, then selling price = 100 + 16 = Rs.116

Cost price of articles is Rs.1, then selling price =

Cost price of articles is Rs.2400, then selling price = = Rs.2784

Hence, Selling Price of 80 articles = Rs.2784

Therefore Selling Price of 1 article

= = Rs.34.80

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

Ans. Here, C.P. = Rs.15,500 and Repair cost = Rs.450

Therefore Total Cost Price = 15500 + 450 = Rs.15,950

Let C.P. be Rs.100, then S.P. = 100 + 15 = Rs.115

When C.P. is Rs.100, then S.P. = Rs.115

When C.P. is Rs.1, then S.P. =

When C.P. is Rs.15950, then S.P.

= = Rs.18,342.50

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.

Ans. Cost price of VCR = Rs.8000 and Cost price of TV = Rs.8000

Total Cost Price of both articles

= Rs.8000 + Rs.8000 = Rs. 16,000

Now VCR is sold at 4% loss.

Let C.P. of each article be Rs.100, then S.P. of VCR = 100 – 4 = Rs.96

When C.P. is Rs.100, then S.P. = Rs.96

When C.P. is Rs.1, then S.P. =

When C.P. is Rs.8000, then S.P.

= = Rs.7,680

And TV is sold at 8% profit, then S.P. of TV = 100 + 8 = Rs.108

When C.P. is Rs.100, then S.P. = Rs.108

When C.P. is Rs.1, then S.P. =

When C.P. is Rs.8000, then S.P.

= = Rs.8,640

Then, Total S.P.

= Rs.7,680 + Rs.8,640 = Rs. 16,320

Since S.P. >C.P.,

Therefore Profit = S.P. – C.P.

= 16320 – 16000 = Rs.320

And Profit% =

== 2%

Therefore,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 Rs.1450and two shirts marked at Rs.850 each?

Ans. Rate of discount on all items = 10%

Marked Price of a pair of jeans = Rs.1450 and Marked Price of a shirt = Rs.850

Discount on a pair of jeans

= = Rs.145

S.P. of a pair of jeans = Rs.1450 – Rs.145 = Rs.1305

Marked Price of two shirts = = Rs.1700

Discount on two shirts = = Rs.170

S.P. of two shirts = Rs.1700 – Rs.170 = Rs.1530

Therefore the customer had to pay = 1305 + 1530

= Discount on a pair of jeans

=

= Rs.145

S.P. of a pair of jeans

= Rs.1450 – Rs.145 = Rs.2,835

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

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)

Ans. S.P. of each buffalo = Rs.20,000

S.P. of two buffaloes = = Rs.40,000

One buffalo is sold at 5% gain.

Let C.P. be Rs.100, then S.P. = 100 + 5 = Rs.105

When S.P. is Rs.105, then C.P. = Rs.100

When S.P. is Rs.1, then C.P. =

When S.P. is Rs.20,000, then C.P.

= = Rs.19,047.62

Another buffalo is sold at 10% loss.

Let C.P. be Rs.100, then S.P. = 100 – 10 = Rs.90

When S.P. is Rs.90, then C.P. = Rs.100

When S.P. is Rs.1, then C.P. =

When S.P. is Rs.20,000, then C.P.

= = Rs.22,222.22

Total C.P. = Rs.19,047.62 + Rs.22,222.22

= Rs.41,269.84

Since C.P. >S.P.

Therefore here it is loss.

Loss = C.P. – S.P.

= Rs.41,269.84 – Rs. 40,000.00 = Rs.1,269.84

The overall loss of milkman was Rs.1269.84

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.

Ans. C.P. = Rs.13,000 and S.T. rate = 12%

Let C.P. be Rs.100, then S.P. for purchaser

= 100 + 12 = Rs.112

When C.P. is Rs.100, then S.P. = Rs.112

When C.P. is Rs.1, then S.P. =

When C.P. is Rs.13,000, then S.P.

= = Rs.14,560

He will have to pay Rs.14,560

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.

Ans. S.P. = Rs.1,600 and Rate of discount = 20%

Let M.P. be Rs.100, then S.P. for customer = 100 – 20 = Rs.80

When S.P. is Rs.80, then M.P. = Rs.100

When S.P. is Rs.1, then M.P. =

When S.P. is Rs.1600, then M.P.

= = Rs.2,000

Thus, the marked price was Rs. 2,000

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

Ans. C.P. = Rs.5,400 and Rate of VAT = 8%

Let C.P. without VAT is Rs. 100, then price including VAT = 100 + 8 = Rs.108

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

When price including VAT is Rs.1, then original price =

When price including VAT is Rs.5400, then original price = = Rs.5000

Thus, the price of Hair Dryer before the addition of VAT was Rs 5000

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

Ans. Given,

GST = 18%

Cost with GST included = Rs. 1239

Cost without GST = x Rs.

x + (18/100 x) = 1239

cost before GST+ GST = cost with GST

x + (9x/50) = 1239

x = 1050

Price before GST = 1050 rupees