B invest his amount in business of A on a condition that B gets 10% of profit as interest on his amount and remaining profit is divided by A and B in equal parts. If at the end of the year A cheats B and take 20% of profit with him and shows remaining profit as actual profit. If remaining profit is distributed between them according to the condition then A gets Rs. 24000 more than B. Find the actual profit that occur at the end of the year.

1. 100000
2. 200000
3. 150000
4. 250000
5. None of these

Option 2 : 200000

Detailed Solution

Solution:

Given: Cheating made by A = 20% of total profit

Difference between the profit amount of A and B = 24000

Calculation: Let the profit at the end of the year = x

A takes 20% of of the overall profit then remaining profit = x × (80/100)

⇒ 0.8x

A takes 10% of the remaining profit as the interest of his investment then remaining profit = 0.8x × (90/100)

⇒ 0.72x

According to the question the remaining profit is divided by them equally, then

A get = 0.36x

B get = 0.36x

B also get 10% of 0.8x, then

Total amount of profit that B has = 0.8x × (10/100) + 0.36x

⇒ 0.08x + 0.36x

⇒ 0.44x

Total amount of profit that A has = x × (20/100) + 0.36x

⇒ 0.20x + 0.36x

⇒ 0.56x

Difference between the amount received by A and B = 0.56x - 0.44x = 24000

⇒ 0.12x = 24000

Total profit occur at the end of the year = x = 200000