Babu sold some ₹ 100 shares at 10% discount and invested his sales proceeds in 15% of ₹ 50 shares at ₹ 33. Had he sold his shares at 10% premium instead of 10% discount, he would have earned ₹ 450 more. Find the number of shares sold by him.

#### Solution

Let the number of shares sold by Babu be x.

The face value of a share is ₹ 100.

He sold a 10% discount; the selling price of one share ₹ 90.

The selling price of x shares = ₹ 90x

He bought a share of face value ₹ 50 and the number of shares 33.

∴ Number of shares bought for the amount ₹ 90x i.e., `(90"x")/33`

∴ Face value of 50 shares = Cost of one share × Number of share

= `50 xx (90"x")/33`

The dividend is 15%.

∴ Income = `15/100` × Face value of 50 shares

= `15/100 xx 50 xx (90"x")/33`

= `(225"x")/11`

Suppose he sold his shares at 10% premium instead of 10% discount, the market value of one share is ₹ 110.

Selling price of x shares = 110 × x = 110x

Number of shares bought for ₹ 33 = `(110"x")/33`

Face value of 50 shares = `(110"x")/33` × 50

Income = `15/100 xx (110"x")/33 xx 50` = 25x

Change Income = ₹ 450

`25"x" = 225/11"x"` = 450

`(25 xx 11"x" - 225"x")/11` = 450

`(275"x" - 225"x")/11` = 450

`(50"x")/11` = 450

x = `450/50 xx 11` = 9 × 11 = 99 shares