## 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.

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?

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.

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.

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.

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?

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)

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.

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.

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.

Let the original price be x.
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.

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.