NCERT Solutions Class 8 Mathematics
Chapter – 8 (Comparing Quantities)
The NCERT Solutions in English Language for Class 8 Mathematics Chapter – 8 Comparing Quantities Exercise 8.2 has been provided here to help the students in solving the questions from this exercise.
Chapter 8: Comparing Quantities
Exercise – 8.2
1. A man got a 10% increase in his salary. If his new salary is ₹1,54,000, find his original salary.
Solution – Let the original salary = x
Given that,
the new salary = ₹1,54,000
Original salary + Increment = New salary
Given that the increment is 10% of the original salary
So, (x + × x) = 154000
x + = 154000
= 154000
x = 154000 × = 140000
Therefore, the original salary was ₹1,40,000.
2. On Sunday, 845 people went to the zoo. On Monday, only 169 people went. What is the per cent decrease in the number of people visiting the zoo on Monday?
Solution –
Given that,
on Sunday went to the zoo = 845 people
on Monday went to the zoo = 169 people
Decrease in the number of people = 845 – 169 = 676
Thus, Percentage decrease = (Decrease in the number of people/Number of people who went to the zoo on Sunday) x 100%
= ( x 100)% = 80%
3. A shopkeeper buys 80 articles for ₹ 2,400 and sells them for a profit of 16%. Find the selling price of one article.
Solution – Given that,
the shopkeeper buys 80 articles = ₹ 2,400
Cost of one article = = ₹ 30
Profit percentage = 16%
Profit percentage = Profit/C.P. x 100
16 = x 100
Profit = = ₹ 4.8
Therefore, the selling price of one article = C.P. + Profit
= ₹ (30 + 4.80)
= ₹ 34.80
4. The cost of an article was ₹ 15,500. ₹ 450 was spent on its repairs. If it is sold for a profit of 15%, find the selling price of the article.
Solution – The total cost of an article = Cost + Overhead expenses
= ₹15500 + ₹450
= ₹15950
Profit percentage = 15%
Profit percentage = Profit/C.P. x 100
15 = x 100
Profit = = 2392.50
Therefore, the selling price of the article = C.P. + Profit
= ₹(15950 + 2392.50)
= ₹18342.50
5. A VCR and TV were bought for ₹ 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 per cent on the whole transaction.
Solution – C.P. of a VCR = ₹ 8000
The shopkeeper made a loss of 4 % on VCR
This means if C.P. is ₹ 100, then S.P. is ₹ 96.
When C.P. is ₹ 8000,
S.P. = x 8000 = ₹ 7680
C.P. of a TV = ₹ 8000
The shopkeeper made a profit of 8 % on TV.
This means that if C.P. is ₹ 100, then S.P. is ₹ 108.
When C.P. is ₹ 8000,
S.P. = x 8000 = ₹ 8640
Total S.P. = ₹ 7680 + ₹ 8640 = ₹ 16320
Total C.P. = ₹ 8000 + ₹ 8000 = ₹ 16000
Since, total S.P.> total C.P. ⇒ profit
Profit = ₹ 16320 − ₹ 16000 = ₹ 320
Profit % on the whole transaction = Profit/Total CP x 100
= x 100 = 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 ₹ 1450 and two shirts marked at ₹ 850 each?
Solution – Total marked price = ₹ (1,450 + 2 × 850)
= ₹ (1,450 +1,700)
= ₹ 3,150
Given that,
the discount percentage = 10%
Discount = ₹ ( x 3150) = ₹ 315
Also, Discount = Marked price − Sale price
₹315 = ₹ 3150 − Sale price
∴ Sale price = ₹ (3150 − 315)
= ₹ 2835
Therefore, the customer will have to pay ₹ 2,835.
7. A milkman sold two of his buffaloes for ₹ 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 the C.P. of each)
Solution – S.P. of each buffalo = ₹ 20,000
The milkman made a gain of 5% while selling one buffalo
This means if C.P. is ₹ 100, then S.P. is ₹ 105.
C.P. of one buffalo = × 20000 = ₹ 19,047.62
Also, the second buffalo was sold at a loss of 10%
This means if C.P. is ₹ 100, then S.P. is ₹ 90
∴ C.P. of other buffalo = × 20000 = ₹ 22222.22
Total C.P. = ₹ 19047.62 + ₹ 22222.22 = ₹ 41269.84
Total S.P. = ₹ 20000 + ₹ 20000 = ₹ 40000
Loss = ₹ 41269.84 − ₹ 40000 = ₹ 1269.84
Therefore, the overall loss of milkman was ₹ 1,269.84
8. The price of a TV is ₹ 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.
Solution – On ₹ 100, the tax to be paid = ₹ 12
Here, on ₹ 13000, the tax to be paid will be = × 13000 = ₹ 1560
Required amount = Cost + Sales Tax
= ₹ 13000 + ₹ 1560
= ₹ 14560
Therefore, Vinod will have to pay ₹ 14,560 for the TV.
9. Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is ₹ 1,600, find the marked price.
Solution – Let the marked price be x
Discount percent = Discount/Marked Price x 100
20 = × 100
Discount = × x =
Also,
Discount = Marked price – Sale price
= x – ₹ 1600
x – = 1600
= 1600
4x = 1600 x 5
x = 2000
Therefore, the marked price was ₹ 2000.
10. I purchased a hair dryer for ₹ 5,400, including 8% VAT. Find the price before VAT was added.
Solution – The price includes VAT
So, 8% VAT means that if the price without VAT is ₹ 100,
Then, the price including VAT will be ₹ 108
When price including VAT is ₹ 108, original price = ₹ 100
When price including VAT is ₹ 5400, original price = ₹ ( × 5400) = ₹ 5000
Therefore, the price of the hair dryer before the addition of VAT was ₹ 5,000.
