Gujarat BoardĀ GSEB Textbook Solutions Class 8 Maths Chapter 8 Comparing Quantities Ex 8.2 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 8 Maths Chapter 8 Comparing Quantities Ex 8.2

Question 1.

A man got a 10% increase in his salary. If his new salary is ā¹ 1,54,000, find his original salary?

Solution:

Let the original salary be ā¹ x

ā“ Increase in salary = 10% of ā¹ x

= ā¹ \(\frac{10}{100}\)x = ā¹ \(\frac{x}{10}\)

New salary = ā¹ x + ā¹ \(\frac{x}{10}\) = ā¹ \(\frac{11}{10}\) x

ā“ ā¹ \(\frac{11}{10}\)x = ā¹ 154000

or x = ā¹ \(\frac{154000Ć10}{11}\) = ā¹ 1,40,000

Thus, the original salary = ā¹ 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?

Solution:

Number of visitors on Sunday = 845

Number of visitors on Monday = 169

Decrease in the number of visitors = 845 – 169 = 676

ā“ Per cent decrease = \(\frac{676}{845}\) Ć 100%

= (4 Ć 20)% = 80%

Question 3.

A shopkeeper buys 80 articles for ā¹ 2,400 and sells them for a profit of 16%. Find the selling price of one article?

Solution:

Cost price = ā¹ 2400

Profit = 16% of ā¹ 2400 = ā¹ \(\frac{16}{100}\) Ć 2400

= ā¹ 16 Ć 24 = ā¹ 384

ā“ Selling price = ā¹ 2400 + ā¹ 384 = ā¹ 2784

Now, selling price per article = ā¹ 2784 + 80

[āµ Number of articles = 80] = ā¹ 34.80

Question 4.

The cost of an article was ā¹ 15,500. ā¹ 450 were spent on its repairs. If it is sold for a profit of 15%, find the selling price of the article?

Solution:

Total cost = ā¹ 15500 + ā¹ 450 (Overhead expenses)

= ā¹ 15950

Profit = 15% of ā¹ 15950

= ā¹ \(\frac{15}{100}\) Ć 15950

= ā¹ \(\frac{15}{100}\) Ć 15950 = ā¹ \(\frac{3Ć1595}{2}\)

= ā¹ \(\frac{4785}{2}\) = ā¹ 2392.50

ā“ Selling price = ā¹ 15950 + ā¹ 2392.50 = ā¹ 18342.50

Question 5.

A VCR and TV were bought for ā¹ 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:

For VCR

CP = ā¹ 8000

Loss = 4% of ā¹ 8000 = ā¹ \(\frac{4}{100}\) Ć 8000 = ā¹ 320

ā“ SP = ā¹ 8000 – ā¹ 320 = ā¹ 7680

Now, total CP = ā¹ 8000 + ā¹ 8000 = 16000 For TV

CP = ā¹ 8000

Profit = 8% of ā¹ 8000 = ā¹ \(\frac{8}{100}\) Ć 8000 = ā¹ 640

SP = ā¹ 8000 + ā¹ 640 = ā¹ 8640

Total SP = ā¹ 7680 + ā¹ 8640 = ā¹ 16320

āµ SP > CP

ā“ Overall profit = ā¹ 16320 – ā¹ 16000 = ā¹ 320

Overall profit per cent = \(\frac{320}{16000}\) Ć 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 ā¹ 1450 and two shirts marked at ā¹ 850 each?

Solution:

For a pair of Jeans

Marked price = ā¹ 1450

Discount = 10% of ā¹ 1450 = ā¹ \(\frac{10}{100}\) Ć 1450 = ā¹ 145

ā“ Sale price = ā¹ 1450 – ā¹ 145 = ā¹ 1305 For two Shirts

Marked price (ā¹ 850) Ć 2 = ā¹ 1700

Discount = 10% of ā¹ 1700

= ā¹ \(\frac{10}{100}\) Ć 1700 = ā¹ 170

ā“ Sale price = ā¹ 1700 – 170 = 1530

Total sale price = ā¹ 1305 + ā¹ 1530 = ā¹ 2835

Thus, the customer would have to pay ā¹ 2835.

Question 7.

A milkman sold two of his buffaloes for ā¹ 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.)

Solution:

For 1st buffalo:

SP = ā¹ 20,000 Profit = 5%

For 2nd buffalo:

SP = ā¹ 20,000 Loss = 10%

ā“ Overall loss = ā¹ (41269.84 – 4000)

= ā¹ 1269.84

Question 8.

The price of a TV is ā¹ 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:

Cost (sale price) of the TV = ā¹ 13,000

Rate of sales tax = 12%

ā“ Sales tax= 12% of ā¹ 13000 = ā¹ \(\frac{12}{100}\) Ć 13000

= ā¹ (12 Ć 130) = ā¹ 1560

ā“ Bill amount = ā¹ 13000 + ā¹ 1560 = ā¹ 14,560

Thus Vinod will have to pay ā¹ 14,560 for the TV.

Question 9.

Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is ā¹ 1,600, find the marked price?

Solution:

Let the marked price = ā¹ 100

ā“ Discount = 20% of ā¹ 100

= ā¹ \(\frac{20}{100}\) Ć 100 = ā¹ 20

Sale price = ā¹ (100 – 20) = ā¹ 80

If sale price is ā¹ 80, then marked price = ā¹ 100

If sale price is ā¹ 1600, then marked price

= ā¹ \(\frac{100}{80}\) Ć 1600 = ā¹ 2000

Question 10.

I purchased a hair-dryer for ā¹ 5,400 including 8% VAT. Find the price before VAT was added?

Solution:

Let the original pricebe ā¹ 100

ā“ Original price + VAT

= ā¹ 100 + ā¹ (8% of 100)

= ā¹ 100 + ā¹ (\(\frac{8}{100}\) Ć 100) = ā¹ 108

ā“ Bill amount = ā¹ 108

If bill amount is ā¹ 108, then original price = ā¹ 100

If bill amount is ā¹ 5,400, then original price

= ā¹ \(\frac{100}{108}\) Ć 5400 = ā¹ (100 Ć 50) = ā¹ 5000