## 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:

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:

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:

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:

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:

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:

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:

Answer:

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:

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:

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:

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:

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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