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: Cost price of buffalo which gave 5% profit
`=(20000)/(105) ×100=20000×(20)/(21)`
Cost price of buffalo which gave 10% loss
`=20000/(90) ×100=20000×(10)/9`
Total cost price
`=2000×(20)/(21)+20000×(10)/9`
`=20000((20)/(21)+(10)/9)`
`=20000((180+210)/(189))=41200` approx
Total Sale Price =2 × 20000 =40000
Loss = 41200 – 40000 = 1200
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`