A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest at the rate of 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?

#### Solution

Let ‘x’ and ‘y’ be the profits earned by A and B respectively and let ‘z’ be the total profit for the year.

A is the working partner and receives ₹ 1500 per month from the total profit

i.e. 12 × 1500 = ₹ 18,000 at the end of the year.

The remaining profit is shared between A and B equally.

∴ y = `("z" - 18000)/2` ........(i)

Thus, profit earned by A at the end of that year is given by

`"x" = 18000 + (("z" - 18000)/2)`

∴ x = `("z" + 18000)/2` ....(ii)

A invests the entire capital on the condition that B pays A interest at the rate of 10% per annum on his half of the capital.

∴ At the end of the first year, A will receive `10/100 xx 25,000` i.e. ₹ 2500/- over and above his share of profit.

∴ A’s income = Profit of A + 2500 = x + 2500

Given that,

the income of A = twice the income of B.

∴ x + 2500 = 2y .....(iii)

Using (i) and (ii) in (iii), we get

`("z" + 18000)/2 + 2500 = 2(("z" - 18000)/2)`

z + 18000 + 5000 = 2(z - 18000)

z + 23000 = 2z − 36000

∴ z = 59,000

∴ The total profit for the year = ₹ 59,000/-