Class 8 - Mathematics
Comparing Quantities - Exercise 8.2
Top Block 1
Question: 1. A man got 10% increase in his salary. If his new salary is Rs.1,54,000, find his original salary.
Answer :
Let original salary be Rs.100.
Therefore New salary i.e., 10% increase
= 100 + 10 = Rs.110
∵ New salary is Rs.110, when original salary = Rs.100
∴ New salary is Rs.1, when original salary = 100⁄110
∴ New salary is Rs.1,54,000, when original salary = 100⁄110 x 154000 = Rs.1,40,000
Hence original salary is Rs. 1,40,000.
Let original salary be Rs.100.
Therefore New salary i.e., 10% increase
= 100 + 10 = Rs.110
∵ New salary is Rs.110, when original salary = Rs.100
∴ New salary is Rs.1, when original salary = 100⁄110
∴ New salary is Rs.1,54,000, when original salary = 100⁄110 x 154000 = Rs.1,40,000
Hence original salary is Rs. 1,40,000.
Question: 2. On Sunday 845 people went to the Zoo. On Monday only 169 people went. What is the percent decrease in the people visiting the Zoo on Monday?
Answer :
On Sunday, people went to the Zoo
= 845
On Monday, people went to the Zoo = 169
Number of decrease in the people
= 845 – 169 = 676
Decrease percent = 676⁄845 = 80%
Hence decrease in the people visiting the Zoo is 80%.
On Sunday, people went to the Zoo
= 845
On Monday, people went to the Zoo = 169
Number of decrease in the people
= 845 – 169 = 676
Decrease percent = 676⁄845 = 80%
Hence decrease in the people visiting the Zoo is 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.
Answer :
No. of articles = 80
Cost Price of articles = Rs. 2,400And Profit
= 16%
∵ Cost price of articles is Rs.100, then selling price = 100 + 16 = Rs.116
∴ Cost price of articles is Rs.1, then selling price = 116⁄100
∴ Cost price of articles is Rs.2400, then selling price = 116⁄100 x 2400 = Rs.2784
Hence, Selling Price of 80 articles = Rs.2784
Therefore Selling Price of 1 article
= 2784⁄80 = Rs.34.80
No. of articles = 80
Cost Price of articles = Rs. 2,400And Profit
= 16%
∵ Cost price of articles is Rs.100, then selling price = 100 + 16 = Rs.116
∴ Cost price of articles is Rs.1, then selling price = 116⁄100
∴ Cost price of articles is Rs.2400, then selling price = 116⁄100 x 2400 = Rs.2784
Hence, Selling Price of 80 articles = Rs.2784
Therefore Selling Price of 1 article
= 2784⁄80 = Rs.34.80
Question: 4. The cost of an article was Rs.15,500, Rs.450 were spent on its repairs. If it sold for a profit of 15%, find the selling price of the article.
Answer :
Here, C.P. = Rs.15,500 and Repair cost = Rs.450
Therefore Total Cost Price = 15500 + 450 = Rs.15,950
Let C.P be Rs.100, then S.P. = 100 + 15
= Rs.115
∵ When C.P. is Rs.100, then S.P. = Rs.115
∴ When C.P. is Rs.1, then S.P. = 115⁄100
∴ When C.P. is Rs.15950, then S.P.
= 115⁄100 x 15950 = Rs.18,342.50
Here, C.P. = Rs.15,500 and Repair cost = Rs.450
Therefore Total Cost Price = 15500 + 450 = Rs.15,950
Let C.P be Rs.100, then S.P. = 100 + 15
= Rs.115
∵ When C.P. is Rs.100, then S.P. = Rs.115
∴ When C.P. is Rs.1, then S.P. = 115⁄100
∴ When C.P. is Rs.15950, then S.P.
= 115⁄100 x 15950 = Rs.18,342.50
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 :
Cost price of VCR = Rs.8000 and Cost price of TV = Rs.8000
Total Cost Price of both articles
= Rs.8000 + Rs.8000 = Rs. 16,000
Now VCR is sold at 4% loss.
Let C.P. of each article be Rs.100, then S.P. of VCR = 100 – 4 = Rs.96
∵ When C.P. is Rs.100, then S.P. = Rs.96
∴ When C.P. is Rs.1, then S.P. = 96⁄100
∴ When C.P. is Rs.8000, then S.P.
= 96⁄100 x 8000 = Rs.7,680
And TV is sold at 8% profit, then S.P. of TV = 100 + 8 = Rs.108
∵ When C.P. is Rs.100, then S.P. = Rs.108
∴ When C.P. is Rs.1, then S.P. = 108⁄100
∴ When C.P. is Rs.8000, then S.P.
= 108⁄100 x 8000 = Rs.8,640
Then, Total S.P.
= Rs.7,680 + Rs.8,640 = Rs. 16,320
Since S.P. > C.P.,
Therefore Profit = S.P. – C.P.
= 16320 – 16000 = Rs.320
And Profit% = Profit⁄Cost Price x 100
= 320⁄16000 x 100 = 2%
Cost price of VCR = Rs.8000 and Cost price of TV = Rs.8000
Total Cost Price of both articles
= Rs.8000 + Rs.8000 = Rs. 16,000
Now VCR is sold at 4% loss.
Let C.P. of each article be Rs.100, then S.P. of VCR = 100 – 4 = Rs.96
∵ When C.P. is Rs.100, then S.P. = Rs.96
∴ When C.P. is Rs.1, then S.P. = 96⁄100
∴ When C.P. is Rs.8000, then S.P.
= 96⁄100 x 8000 = Rs.7,680
And TV is sold at 8% profit, then S.P. of TV = 100 + 8 = Rs.108
∵ When C.P. is Rs.100, then S.P. = Rs.108
∴ When C.P. is Rs.1, then S.P. = 108⁄100
∴ When C.P. is Rs.8000, then S.P.
= 108⁄100 x 8000 = Rs.8,640
Then, Total S.P.
= Rs.7,680 + Rs.8,640 = Rs. 16,320
Since S.P. > C.P.,
Therefore Profit = S.P. – C.P.
= 16320 – 16000 = Rs.320
And Profit% = Profit⁄Cost Price x 100
= 320⁄16000 x 100 = 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.1450and two shirts marked at Rs.850 each?
Answer :
Rate of discount on all items = 10%
Marked Price of a pair of jeans = Rs.1450 and Marked Price of a shirt = Rs.850
Discount on a pair of jeans
= (Rate x M.P.)⁄100 x 100 = (10 x 1450)⁄100 x 100 = Rs.145
∴ S.P. of a pair of jeans = Rs.1450 – Rs.145
= Rs.1305
Marked Price of two shirts = 2 x 850
= Rs.1700
Discount on two shirts = (Rate x M.P.)⁄100 x 100 = (10 x 1700)⁄100 x 100
= Rs.170
∴ S.P. of two shirts = Rs.1700 – Rs.170
= Rs.1530
Therefore the customer had to pay
= 1305 + 1530
= Discount on a pair of jeans
= (Rate x M.P.)⁄100 x 100 = (10 x 1450)⁄100 x 100
= Rs.145
S.P. of a pair of jeans
= Rs.1450 – Rs.145 = Rs.2,835
Rate of discount on all items = 10%
Marked Price of a pair of jeans = Rs.1450 and Marked Price of a shirt = Rs.850
Discount on a pair of jeans
= (Rate x M.P.)⁄100 x 100 = (10 x 1450)⁄100 x 100 = Rs.145
∴ S.P. of a pair of jeans = Rs.1450 – Rs.145
= Rs.1305
Marked Price of two shirts = 2 x 850
= Rs.1700
Discount on two shirts = (Rate x M.P.)⁄100 x 100 = (10 x 1700)⁄100 x 100
= Rs.170
∴ S.P. of two shirts = Rs.1700 – Rs.170
= Rs.1530
Therefore the customer had to pay
= 1305 + 1530
= Discount on a pair of jeans
= (Rate x M.P.)⁄100 x 100 = (10 x 1450)⁄100 x 100
= Rs.145
S.P. of a pair of jeans
= Rs.1450 – Rs.145 = Rs.2,835
Mddle block 1
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. (Hint: Find CP of each)
Answer :
S.P. of each buffalo = Rs.20,000
S.P. of two buffaloes = 20000 x 2
= Rs.40,000
One buffalo is sold at 5% gain.
Let C.P. be Rs.100, then S.P. = 100 + 5
= Rs.105
∵ When S.P. is Rs.105, then C.P. = Rs.100
∴ When S.P. is Rs.1, then C.P. = 105⁄100
∴ When S.P. is Rs.20,000, then C.P.
= 105⁄100 x 20000 = Rs.19,047.62
Another buffalo is sold at 10% loss.
Let C.P. be Rs.100, then S.P. = 100 – 10
= Rs.90
∵ When S.P. is Rs.90, then C.P. = Rs.100
∴ When S.P. is Rs.1, then C.P. = 100⁄90
∴ When S.P. is Rs.20,000, then C.P.
= 100⁄90 = Rs.22,222.22
Total C.P. = Rs.19,047.62 + Rs.22,222.22
= Rs.41,269.84
Since C.P. > S.P.
Therefore here it is loss.
Loss = C.P. – S.P.
= Rs.41,269.84 – Rs. 40,000.00 = Rs.1,269.84
S.P. of each buffalo = Rs.20,000
S.P. of two buffaloes = 20000 x 2
= Rs.40,000
One buffalo is sold at 5% gain.
Let C.P. be Rs.100, then S.P. = 100 + 5
= Rs.105
∵ When S.P. is Rs.105, then C.P. = Rs.100
∴ When S.P. is Rs.1, then C.P. = 105⁄100
∴ When S.P. is Rs.20,000, then C.P.
= 105⁄100 x 20000 = Rs.19,047.62
Another buffalo is sold at 10% loss.
Let C.P. be Rs.100, then S.P. = 100 – 10
= Rs.90
∵ When S.P. is Rs.90, then C.P. = Rs.100
∴ When S.P. is Rs.1, then C.P. = 100⁄90
∴ When S.P. is Rs.20,000, then C.P.
= 100⁄90 = Rs.22,222.22
Total C.P. = Rs.19,047.62 + Rs.22,222.22
= Rs.41,269.84
Since C.P. > S.P.
Therefore here it is loss.
Loss = C.P. – S.P.
= Rs.41,269.84 – Rs. 40,000.00 = Rs.1,269.84
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 :
C.P. = Rs.13,000 and S.T. rate = 12%
Let C.P. be Rs.100, then S.P. for purchaser
= 100 + 12 = Rs.112
∵ When C.P. is Rs.100, then S.P. = Rs.112
∴ When C.P. is Rs.1, then S.P. = 112⁄100
∴ When C.P. is Rs.13,000, then S.P.
= 112⁄100 = Rs.14,560
C.P. = Rs.13,000 and S.T. rate = 12%
Let C.P. be Rs.100, then S.P. for purchaser
= 100 + 12 = Rs.112
∵ When C.P. is Rs.100, then S.P. = Rs.112
∴ When C.P. is Rs.1, then S.P. = 112⁄100
∴ When C.P. is Rs.13,000, then S.P.
= 112⁄100 = Rs.14,560
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 :
S.P. = Rs.1,600 and Rate of discount
= 20%
Let M.P. be Rs.100, then S.P. for customer
= 100 – 20 = Rs.80
∵ When S.P. is Rs.80, then M.P. = Rs.100
∴ When S.P. is Rs.1, then M.P. = 100⁄80
∴ When S.P. is Rs.1600, then M.P.
= 100⁄80 x 1600 = Rs.2,000
S.P. = Rs.1,600 and Rate of discount
= 20%
Let M.P. be Rs.100, then S.P. for customer
= 100 – 20 = Rs.80
∵ When S.P. is Rs.80, then M.P. = Rs.100
∴ When S.P. is Rs.1, then M.P. = 100⁄80
∴ When S.P. is Rs.1600, then M.P.
= 100⁄80 x 1600 = Rs.2,000
Question: 10. I purchased a hair-dryer for Rs.5,400 including 8% VAT. Find the price before VAT was added.
Answer :
C.P. = Rs.5,400 and Rate of VAT = 8%
Let C.P. without VAT is Rs. 100, then price including VAT = 100 + 8 = Rs.108
∵ When price including VAT is Rs.108, then original price = Rs.100
∴ When price including VAT is Rs.1, then original price = 100⁄108
∴ When price including VAT is Rs.5400, then original price = 100⁄108 x 5400 = Rs.5000
C.P. = Rs.5,400 and Rate of VAT = 8%
Let C.P. without VAT is Rs. 100, then price including VAT = 100 + 8 = Rs.108
∵ When price including VAT is Rs.108, then original price = Rs.100
∴ When price including VAT is Rs.1, then original price = 100⁄108
∴ When price including VAT is Rs.5400, then original price = 100⁄108 x 5400 = Rs.5000