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Comparing Quantities : Exercise 8.2 (Mathematics NCERT Class 8th)


Q.1 A man got a 10% increase in his salary. If his new salary is Rs 1,54,000, find his original salary.
Sol. Let the original salary be x.
Given, the new salary is Rs 1,54,000 and increment is 10% of the original salary.
Therefore, Original Salary + Increment = New Salary
x + {{10} \over {100}} \times x = 1,54,000
{{110x} \over {100}} = 1,54,000
x = \left( {154000 \times {{100} \over {110}}} \right)
x = 1,40,000
Hence, the original salary was Rs 1,40,000.

Q.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?
Sol. Given, 845 people went to the zoo on Sunday and 169 people went on Monday.
Therefore, decrease in the number of people = 845 – 169 = 676
Percentage decrease = \left( {{{676} \over {845}} \times 100} \right)\% = 80%
Hence, there is decrease of 80% in the people visiting Zoo on Monday.

Q.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.
Sol. Given, shopkeeper buys 80 articles for Rs 2,400.
Therefore, cost of one article = Rs{{2400} \over {80}}= Rs 30
Also, given profit percent = 16.
Therefore, Profit percent = (Profit/C. P.) x 100
16 = {{{\rm{Profit}}} \over {30}} \times 100
Profit = Rs \left( {{{16 \times 30} \over {100}}} \right)= Rs 4.80
Hence, selling price of one article = C.P. + Profit = Rs (30 + 4.80) = Rs 34.80

Q.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.
Sol. We know that, total cost of an article = cost + other expenses
= Rs 15500 + Rs 450
= Rs 15950
Therefore, Profit % = {{{\rm{Profit}}} \over {{\rm{C}}{\rm{.P}}{\rm{.}}}} \times 100
15 = {{{\rm{Profit}}} \over {{\rm{Rs }}15950}} \times 100
Profit = Rs\left( {{{15950 \times 15} \over {100}}} \right)= Rs 2392.50
Thus, selling price of the article = C.P. + Profit = Rs 15950 + Rs 2392.50 = Rs 18342.50

Q.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.
Sol. Given, C.P. of VCR = Rs 8000 and shopkeeper made a loss of 4% on it.
Hence, it means that if C.P. is Rs 100, then S.P. is Rs 96
For C.P. of Rs 8000, S.P. = Rs \left( {{{96 \times 8000} \over {100}}} \right)= Rs 7680
Given, C.P. of TV = Rs 8000 and shopkeeper made a profit of 8% on it.
Hence, it means that if C.P. is Rs 100, then S.P. is Rs 108
For C.P. of Rs 8000, S.P. = Rs \left( {{{108 \times 8000} \over {100}}} \right)= Rs 8640
Now, total S.P. of VCR and TV = Rs 7680 + Rs 8640 = Rs 16320
And total C.P. of VCR and TV = Rs 8000 + Rs 8000 = Rs 16000
Here, total S.P. is greater than total C.P., which means there is profit made.
Therefore, Profit = Rs 16320 – Rs 16000 = Rs 320
Profit % = {{{\rm{Profit}}} \over {{\rm{C}}{\rm{.P}}{\rm{.}}}} \times 100
= {{{\rm{320}}} \over {16000}} \times 100
= 2 %
Hence, the shopkeeper had a 2% gain on the whole transaction.

Q.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?Sol. Given, price of jeans = Rs 1450
Price of two shirts = 2 x Rs 850 = Rs 1400
Therefore, total marked price = Rs 1450 + Rs 1400 = Rs 3150
Given, discount offered is 10%.
Discount = Rs \left( {{{10} \over {100}} \times 3150} \right)= Rs 315
Now, Discount = Marked price – Sale price
Rs 315 = Rs 3150 – Sale Price
Therefore, Rs (3150 – 315) = Rs 2835
Hence, customer would have to pay Rs 2835.

Q.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)
Sol. Given, S.P. of first buffalo = Rs 20000 and profit made was 5%.
Hence, it means that if C.P. is Rs 100, then S.P. is Rs 105
Therefore, C.P. of first buffalo = \left( {20000 \times {{100} \over {105}}} \right)= Rs 19,047.62
Given, S.P. of second buffalo = Rs 20000 and loss made was 10%.
Hence, it means that if C.P. is Rs 100, then S.P. is Rs 90
Therefore, C.P. of second buffalo = \left( {20000 \times {{100} \over {90}}} \right)= Rs 22,222.22
Now, total C.P. of both buffaloes = Rs 19047.62 + Rs 22222.22 = Rs 41,269.84
And total S.P. of both buffaloes = Rs 20000 + Rs 20000 = Rs 40000
Here, total C.P. is greater than total S.P., which means there is loss made.
Therefore, Loss = Rs 41269.84 – Rs 40000 = Rs 1269.84
Hence, overall loss of milkman is Rs 1,269.84

Q.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.
Sol. Given, sales tax charged on TV is at the rate of 12%. It means that, on Rs 100 the tax to be paid will be Rs 12.
Therefore, tax to be paid on TV = Rs \left( {{{12} \over {100}} \times 13000} \right) = Rs 1,560
Required amount = C.P. + Tax = Rs 13000 + Rs 1560 = Rs 14,560
Hence, Vinod will have to pay Rs 14,560 for the TV.

Q.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.
Sol. Let the marked price be x.
{\rm{Discount \% = }}{{{\rm{Discount}}} \over {{\rm{Marked price}}}} \times 100
{\rm{20 = }}{{{\rm{Discount}}} \over x} \times 100
Discount = {{{\rm{20}}} \over {100}} \times x= {1 \over 5}x
We know that, Discount = Marked Price – Sale Price
{1 \over 5}x = x - {\rm{Rs }}1600
x - {1 \over 5}x = {\rm{Rs }}1600
{4 \over 5}x = {\rm{Rs }}1600
x = {\rm{Rs }}\left( {1600 \times {5 \over 4}} \right)= Rs 2000
Hence, the marked price was Rs 2000.

Q.10 I purchased a hair-dryer for Rs 5,400 including 8% VAT. Find the price before VAT was added.
Sol. Given, the price of Rs 5400 includes 8% VAT.
Thus, it means that if the price without VAT is Rs 100, then price including VAT will be Rs 108.
Therefore, for price Rs 5400 including VAT, original price = {\rm{Rs }}\left( {{{100} \over {108}} \times 5400} \right)= Rs 5000
Hence, the price before VAT was added is Rs 5,000.



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