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.

Answer: CP = Cost + Overheads
`= 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`



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