Question

₹ 50 shares of a company are bought by John at 20% discount and sold at the gain of 25%.

Assertion (A): The net gain on each share is 5%.

Reason (R): For John, The selling price of each share = `₹50 × 80/100 × 125/100`

Options

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

A is false, R is true.

Explanation:

Face value of share = ₹ 50

Discount = 20%

Discounted value = 20% of ₹ 50

= `20/100 xx 50`

= ₹ 10 

Discounted price = ₹ 50 − ₹ 10 = ₹ 40

Gain = 25%

Selling price = ₹ 40 + 25% of ₹ 40

= `₹ 40 + 25/100 × 40`

= ₹ (40 + 10)

= ₹ 50

Gain = ₹ 50 − ₹ 40

= ₹ 10

Gain % = `"Gain"/(CP) × 100`

= `10/40 xx 100`

= 25%

So, Assertion (A) is false.

As per the Reason (R),

The selling price of each share = `₹50 × 80/100 × 125/100`

= ₹ (50 × 0.8 × 1.25)

= ₹ 50

This is equal to the selling price computed above.

So, Reason (R) is true.

Hence, option 2 is correct.