Profit, Loss and Discount — Assertion Reason Type Questions

Assertion (A): Ajay sold his laptop for ₹ 25,000 at a profit of ₹ 2,250. Ajay's profit % is 9%.

Reason (R): Profit % = $\left(\dfrac{\text{Profit}}{\text{C.P.}} \times 100\right)$%

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

S.P. = ₹ 25,000 and profit = ₹ 2,250.

C.P. = S.P. − profit = 25,000 − 2,250 = ₹ 22,750.

Profit% = $\left(\dfrac{\text{profit}}{\text{C.P.}} \times 100\right)$%

= $\left(\dfrac{2,250}{22,750} \times 100\right)$%

= $\dfrac{900}{91}$%

= 9.89% (approx.), which is not 9%.

So, Assertion (A) is false.

Profit % = $\left(\dfrac{\text{Profit}}{\text{C.P.}} \times 100\right)$% is the correct formula.

So, Reason (R) is true.

Hence, option 2 is the correct option.

Assertion (A): A bicycle marked at ₹ 12,500 is sold for ₹ 10,500. Discount offered by the shopkeeper is 16%.

Reason (R): Discount % = $\left(\dfrac{\text{Discount}}{\text{C.P.}} \times 100\right)$%

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

Marked price = ₹ 12,500 and S.P. = ₹ 10,500.

Discount = M.P. − S.P. = 12,500 − 10,500 = ₹ 2,000.

Discount% = $\left(\dfrac{\text{discount}}{\text{M.P.}} \times 100\right)$%

= $\left(\dfrac{2,000}{12,500} \times 100\right)$%

= 16%

So, Assertion (A) is true.

Discount % is calculated on the marked price, not on the C.P. The correct formula is Discount % = $\left(\dfrac{\text{Discount}}{\text{M.P.}} \times 100\right)$%.

So, Reason (R) is false.

Hence, option 1 is the correct option.

Assertion (A): A shopkeeper buys 100 bicycles at ₹ 1,000 each. He spends ₹ 1,000 on transportation and paid ₹ 400 on road tax. He sells all the bicycles at ₹ 1,050 each. Thus he is making a profit of ₹ 3,000.

Reason (R): If an article is purchased for some amount and there are some additional expenses on transportation, labour, tax, etc., then these expenses are added to get the total cost price.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

Total C.P. = (100 × 1,000) + 1,000 + 400 = 1,00,000 + 1,400 = ₹ 1,01,400.

Total S.P. = 100 × 1,050 = ₹ 1,05,000.

Profit = 1,05,000 − 1,01,400 = ₹ 3,600, which is not ₹ 3,000.

So, Assertion (A) is false.

If an article is purchased for some amount and there are some additional expenses on transportation, labour, tax, etc., then these expenses are added to the purchase price to get the total cost price. This is correct.

So, Reason (R) is true.

Hence, option 2 is the correct option.

Assertion (A): The price of a jacket was ₹ 960 in the month of December. The same jacket is available in off season at ₹ 816. Off season discount % is 15%.

Reason (R): Marked price (M.P.) is the price that is printed on the article.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

Marked price = ₹ 960 and off-season price = ₹ 816.

Discount = 960 − 816 = ₹ 144.

Discount% = $\left(\dfrac{\text{discount}}{\text{M.P.}} \times 100\right)$%

= $\left(\dfrac{144}{960} \times 100\right)$%

= 15%

So, Assertion (A) is true.

Marked price (M.P.) is the price that is printed on the article. This is correct.

So, Reason (R) is true.

Hence, option 3 is the correct option.