NCERT Solutions Class 7 Mathematics Comparing Quantities Ex 8.3

Question: 1.Tell what is the profit or loss in the following transactions. Also find profit percent or loss percent in each case.

(a) Gardening shears bought for Rs. 250 and sold for Rs. 325.

(b) A refrigerator bought Rs. 12,000 and sold at Rs. 13,500.

(c) A cupboard bought for Rs. 2,500 and sold at Rs. 3,000.

(d) A skirt bought for Rs. 250 and sold at Rs. 150.

Answer :
(a) Cost price of gardening shears = Rs. 250

Selling price of gardening shears = Rs. 325

Since, S.P. > C.P., therefore here is profit.

∴ Profit = S.P. – C.P. = 325 – 250 = Rs. 75

Now Profit% = ^Profit⁄_C.P. × 100

= ⁷⁵⁄₂₅₀ × 100 = 30%

Therefore, Profit = Rs. 75 and Profit% = 30%

(b) Cost price of refrigerator = Rs. 12,000

Selling price of refrigerator = Rs. 13,500

Since, S.P. > C.P., therefore here is profit.

∴ Profit = S.P. – C.P. = 13500 – 12000 = Rs. 1,500

Now Profit% = ^Profit⁄_C.P. × 100

= ¹⁵⁰⁰⁄₁₂₀₀₀ = 12.5%

Therefore, Profit = Rs. 1,500 and Profit% = 12.5%

(c) Cost price of cupboard = Rs. 2,500

Selling price of cupboard = Rs. 3,000

Since, S.P. > C.P., therefore here is profit.

∴ Profit = S.P. – C.P. = 3,000 – 2,500 = Rs. 500

Now Profit% = ^Profit⁄_C.P. × 100

= ⁵⁰⁰⁄₂₅₀₀ × 100 = 20%

Therefore, Profit = Rs. 500 and Profit% = 20%

(d) Cost price of skirt = Rs. 250

Selling price of skirt = Rs. 150

Since, C.P. > S.P., therefore here is loss.

∴ Loss = C.P. – S.P. = 250 – 150 = Rs. 100

Now Loss% = ^Loss⁄_C.P. ×100

= ¹⁰⁰⁄₂₅₀ × 100 = 40%

Therefore, Profit = Rs. 100 and Profit% = 40%

Question: 2.Convert each part of the ratio to percentage:

(a) 3 : 1

(b) 2 : 3 : 5

(c) 1 : 4

(d) 1 : 2 : 5

Answer :
(a) 3 : 1

Total part = 3 + 1 = 4

Therefore, Fractional part = ³⁄₄:¹⁄₄

⇒ Percentage of parts = ³⁄₄×100 : ¹⁄₄ × 100

⇒ Percentage of parts = 75% : 25%

(b) 2 : 3 : 5

Total part = 2 + 3 + 5 = 10

Therefore, Fractional part = ²⁄₁₀ : ³⁄₁₀ : ⁵⁄₁₀

⇒ Percentage of parts = ²⁄₁₀ × 100 : ³⁄₁₀ × 100 : ⁵⁄₁₀ × 100

⇒ Percentage of parts = 20% : 30% : 50%

(c) 1 : 4

Total part = 1 + 4 = 5

Therefore, Fractional part = ¹⁄₅ : ⁴⁄₅

⇒ Percentage of parts = ¹⁄₅ × 100 : ⁴⁄₅ × 100

⇒ Percentage of parts = 20% : 80%

(d) 1 : 2 : 5

Total part = 1 + 2 + 5 = 8

Therefore, Fractional part = ¹⁄₈18 : ²⁄₈ : ⁵⁄₈

⇒ Percentage of parts = ¹⁄₈ × 100 : ²⁄₈ × 100 : ⁵⁄₈ × 100

⇒ Percentage of parts = 12.5% : 25% : 62.5%

Question: 3.The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.

Answer :
The decreased population of a city from 25,000 to 24,500.

Population decreased = 25,000 – 24,500 = 500

Decreased Percentage = ^{Population decreased}⁄_{Original population} × 100

= ⁵⁰⁰⁄₂₅₀₀₀ × 100 = 2%

Hence, the percentage decreased is 2%.

Question: 4.Arun bought a car for Rs. 3,50,000. The next year, the price went up to Rs. 3,70,000. What was the percentage of price increase?

Answer :
Increased in price of a car from Rs. 3,50,000 to Rs. 3,70,000.

Amount change = Rs. 3,70,000 – Rs. 3,50,000 = Rs. 20,000.

Therefore, Increased percentage = ^{Amount of change}⁄_{Original amount}×100

= ²⁰⁰⁰⁰⁄₃₅₀₀₀₀ × 100 = 5⁵⁄₇%

Hence, the percentage of price increased is 5⁵⁄₇%.

Question: 5. I buy a T.V. for Rs. 10,000 and sell it at a profit of 20%. How much money do I get for it?

Answer :
The cost price of T.V. = Rs. 10,000

Profit percent = 20%

Now, Profit = Profit% of C.P.

= ²⁰⁄₁₀₀ × 10000 = Rs. 2,000

Selling price = C.P. + Profit

= 10,000 + 2,000 = Rs. 12,000

Hence, he gets Rs. 12,000 on selling his T.V.

Question: 6.Juhi sells a washing machine for Rs. 13,500. She loses 20% in the bargain. What was the price at which she bought it?

Answer :
Selling price of washing machine = Rs. 13,500

Loss percent = 20%

Let the cost price of washing machine be Rs.x.

Since, Loss = Loss% of C.P.

⇒ Loss = 20% of Rs. 𝓍 = ²⁰⁄₁₀₀ × 𝓍 = ^𝓍⁄₅

Therefore, S.P. = C.P. – Loss

⇒ 13500 = 𝓍 – ^𝓍⁄₅ ⇒ 13500 = ^4𝓍⁄₅

⇒ 𝓍 = 13500 × ⁵⁄₄ = Rs. 16,875

Hence, the cost price of washing machine is Rs. 16,875.

Question: 7.(i) Chalk contains Calcium, Carbon and Oxygen in the ratio 10 : 3 : 12. Find the percentage of Carbon in chalk.

(ii) If in a stick of chalk, Carbon is 3 g, what is the weight of the chalk stick?

Answer :
(i) Given ratio = 10 : 3 : 12

Total part = 10 + 3 + 12 = 25

Part of Carbon = ³⁄₂₅

Percentage of Carbon part in chalk = ³⁄₂₅ ×100 = 12%

(ii) Quantity of Carbon in chalk stick = 3 g

Let the weight of chalk be x g.

Then, 12% of 𝓍 = 3

⇒ ¹²⁄₁₀₀ × 𝓍=3 ⇒ 𝓍 = 3 × ¹⁰⁰⁄₁₂ = 25 g

Hence the weight of chalk stick is 25 g.

Question: 8.Amina buys a book for Rs. 275 and sells it at a loss of 15%. How much does she sell it for?

Answer :
The cost of a book = Rs. 275

Loss percent = 15%

Loss = Loss% of C.P. = 15% of Rs. 275

= ¹⁵⁄₁₀₀ × 275 = Rs. 41.25

Therefore, S.P. = C.P. – Loss

= 275 – 41.25 = Rs. 233.75

Hence, Amina sells a book for Rs. 233.75.