NCERT Class 8 Maths Chapter 8 Comparing Quantities Exercise 8.2

Chapter 8 Comparing Quantities Exercise 8.2

Question 1: A man got a 10% increase in his salary. If his new salary is ₹1,54,000, find his original salary.
Answer:

Increase% = 10%
New Salary = ₹1,54,000
Original Salary = ?

Let the original salary be x.
New salary = x + 10% of x
= 1,54,000 = x + 10/100 × x
= 1,54,000 = x + 10x/100
= 1,54,000 = 10x/10 + 1x/10
= 1,54,000 = 11x/10
= 11x = 1,54,000 × 10
= 11x = 15,40,000
= x = 15,40,000/11
= x = 1,40,000

Therefore, his original salary was 1,40,000.

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:

Number of people who went to zoo on Sunday = 845
Number of people who went to zoo on Monday = 169
Difference = 845 - 169 = 676

Decrease% = Change/Original × 100
Decrease% = 676/845 × 100
                   = 67600/845
                   = 80%

Therefore, the decrease per cent in the people visiting the zoo on Monday is 80%.

Question 3: A shopkeeper buys 80 articles for ₹2,400 and sells them for a profit of 16%. Find the selling price of one article.
Answer:

Cost of 80 articles = ₹2,400
Cost of 1 article = 2,400/80 = 30
Profit% = 16%

Selling price of 1 article = 30 + 16% of 30
= 30 + 16/100 × 30
= 30 + 480/100
= 300/10 + 48/10
= 348/10
= 34.8

Selling Price = ₹34.8

Therefore, the selling price of one article is ₹34.8.

Question 4: The cost of an article was ₹15,500. ₹450 were spent on its repairs. If it is sold for a profit of 15%, find the selling price of the article.
Answer:

Cost of an article = ₹15,500
Repair charge = ₹450
Profit% = 15%
Selling Price = 15,500 + 15% of 15,950
                     = 15,950 + 15/100 × 15,950
                     = 15,950 + 15 × 319/2
                     = 15,950 + 2392.5
                     = 18,342.5

Therefore, the selling price of the article was ₹18,342.5.

Question 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 percent on the whole transaction.
Answer:

VCR
Cost Price = ₹8,000
Loss% = 4%
Selling Price = 8,000 - 4/100 × 8000
                     = 8,000 - 4 × 80
                     = 8,000 - 320
                     = 7,680

TV
Cost Price = ₹8,000
Profit% = 8%
Selling Price = 8,000 + 8/100 × 8,000
                     = 8,000 + 8 × 80
                     = 8,000 + 640
                     = 8,640

Total Cost Price = ₹16,000
Selling Price = ₹7,680 + ₹8,640 = ₹16,320
Selling Price > Cost Price = Profit

Profit = 16,320 - 16,000 = 320

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 ₹1450 and two shirts marked at ₹850 each?
Answer:

Cost Price of pair of jeans = ₹1450
Cost Price of 2 shirts = ₹850 (for one)
                                   = ₹850 + ₹850 = ₹1700

Total Cost Price (Jeans + 2 Shirt CP) = ₹1450 + ₹1700
                                                             = ₹3150

Discount% = 10%
Selling Price = 3150 - 10% of 3150
                      = 3150 - 10/100 × 3150
                      = ₹3150 - ₹315 = ₹2835

Therefore, the customer has to pay ₹2835 for a pair of jeans and two shirts.

Question 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 CP of each)
Answer:


Total Selling Price = ₹40,000
Total Cost Price = ₹41,269.83

Cost Price > Selling Price = Loss
Loss = ₹41,269.83 - ₹40,000 = ₹1,269.83

Therefore, there is a loss by ₹1269.83.

Question 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.
Answer:

Cost Price of TV = ₹13,000
Tax% = 12%

Amount to be paid = 13000 + 12% of 13000
                               = 13000 + 12/100 × 13000
                               = 13000 + 1560
                               = ₹14,560

Therefore, the amount that Vinod will have to pay if he buys the TV will be ₹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 ₹1,600, find the marked price.
Answer:

Discount% = 20%
Amount paid = ₹1600
Marked Price = ?

Let the Marked Price be x.
= x - 20% of x = 1600
= x/1 - 20x/100 = 1600
= 5x/5 - x/5 = 1600
= 4x/5 = 1600
= 4x = 1600 × 5
= 4x = 8000
= x = 8000/4
= x = 2000

Therefore, the marked price of the article is ₹2,000.

Question 10: I purchased a hair-dryer for ₹5,400 including 8% VAT. Find the price before VAT was added.
Answer:

Let the original price be x.
Value Added Tax = 8%
Amount paid = ₹5400

= x + 8% of x = ₹5400
= x/1 + 8x/100 = 5400
= 25x/25 + 2x/25 = 5400
= 27x/25 = 5400
= 27x = 5400 × 25
= 27x = 135000
= x = 135000/27
= x = 5000

Therefore, the cost of hair-dryer will be ₹5,000 before the VAT was added.

Question 11: An article was purchased for ₹1239 including the GST of 18%. Find the price of the article before GST was added.
Answer:

Let the original price of the article be x.
Total amount paid = ₹1239

= x + 18% of x = ₹1239
= x/1 + 18x/100 = 1239
= 50x/50 + 9x/50 = 1239
= 59x/50 = 1239
= 59x = 1239 × 50
= 59x = 61950
= x = 61950/59
= x = ₹1050

Therefore, the cost of the article before the GST was added was ₹1050.

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