# Comparing Quantities

## 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.

Answer: Let us assume the initial salary =100
So, salary after hike = 100+100 10%=100+10=110

∵ When increased salary is 110, then initial salary is 100

∴ When increased salary is 1, the initial salary is (100)/(110)

∴ When increased salary is 154000, the initial salary is (100)/(110)xx154000=140000

Alternate Method:

The question can be solved by assuming x for initial salary, as follows:

x\xx(110)/(100)=154000

Or, x=154000xx(100)/(110)=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?

Answer: Actual decrease in number of visits
= 845-169=676

Percentage Decrease =(676)/(845)xx100=80%

Alternate Method:

∵ When original number of visitors is 845, the decrease is 676

∴ When original number of visitors is 1, the decrease is (676)/(845)

∴ When original number of visitors is 100, the decrease is (676)/(845)xx100=80%

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.
Profit = CP x % profit

=2400xx(16)/(100)=384

So, Sp = CP + Profit

=2400+384=2780

SP of one article =(2784)/(80)=34.80

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.

= 15500 + 450 = 15950
Profit = CP xx % profit

Profit = CP xx % profit

=15950xx(15)/(100)=2392.50

So, SP = CP+Profit
= 15950 + 2392.50 = 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.

Answer: Loss on VCR = CP xx &% Loss

=8000xx(4)/(100)=320

Profit on TV = CP xx % Profit

=8000xx(8)/(100)=640

Overall Profit =640-320=320

Percentage Profit =text(Profit)/text(CP)xx100

=(320)/(16000)xx100=2%

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?

Answer: Total Price of a pair of jeans and two shirts
= 1450 + 2 xx 850 = 3150
Discount = Marked Price xx % Discount

=3150xx(10)/(100)=315

Effective Price After Discount = 3150 - 315 = 2835

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.

Answer: Suppose the CP of each buffalo = 100
After 5% profit, SP = 105
After 10% loss SP = 90

In case of profitable deal, CP =20000xx(100)/(105)

=20000xx(20)/(21)

Net Profit =20000-20000xx(20)/(21)

=(420000-400000)/(21)=(20000)/(21)

In case of loss making deal, CP =20000xx(100)/(95)

=20000xx(20)/(19)

Net Loss =20000xx(20)/(19)-20000

=(400000-380000)/(19)=(20000)/(19)

Overall Profit/Loss =(20000)/(21)-(20000)/(19)

=(380000-420000)/(399)=(40000)/(399)

As 399≈400, so net loss is approx. Rs. 1000

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.

Answer: Sales Tax = Price xx Tax Rate

=13000xx(12)/(100)=1560

Final Price = 13000 + 1560 = 14560

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.

Answer: Marked Price = (100)/(100-text(Discount))xx\text(Marked Price)

=(100)/(100-20)xx1600

=(100)/(80)xx1600=2000

Alternate Method:

∵ When final price is 80, then marked price is 100

∴ When final price is 1, then marked price is (100)/(80)

∴ When final price is 1600, then marked price is (100)/(80)xx1600=2000

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

Answer: Price before VAT =(100)/(100+text(VAT))xx\text(Final Price)

=(100)/(108)xx5400=5000