Question

Q.9) A, B and C invest Rs. 4000, Rs. 5000 and
RS. 6000 respectively in a business and A gets
25% of profit for managing the business, the rest
of the profit is divided by A, B and C in proportion
to their investment. If in a year, A gets Rs. 200
less than B and C together, what was the total
profit of that year?
a) Rs. 1000 b) Rs. 1500 c) Rs. 1800
d) Rs. 2000 e) Rs. 2200​

Answer 1

a) 1000

A = 0.25 P + 0.75P * 4/15

= 0.45

B = 0.75P * 5/15

= 0.25

C = 0.75P * 6/15

= 0.3

So,

0.55 P - 0.45 P = 0.1 P

= 100

Profit = 1000

Answer 2

The correct option would be d) Rs. 2000

Step-by-step explanation:

Given,

Investment of,

A = 4000 rupees,

B = 5000 rupees,

C = 6000 rupees,

∵ Time is same for all,

So, profit ∝ investment,

Thus, the ratio of profit of A, B and C = 4000 : 5000 : 6000

= 4 : 5 : 6

Let A's share = 4x, B's hare = 5x and C's share = 6x,

Where, x is any positive real number,

Total profit which they divided = 4x + 5x + 6x = 15x,

∵ A gets 25% of profit for managing the business and rest is divided by A, B and C in proportion to their investment.,

Thus, 75% of total profit = 15x,

⇒ $\frac{75}{100}\text{ of total profit}=15x$

⇒ Total profit = $\frac{15x\times 100}{75}=\frac{100x}{5}=20x$,

Now, A's total share = 25% of 20x + 4x

= 5x + 4x

= 9x,

While, B and C's combined share = 5x + 6x = 11x,

According to the question,

11x - 9x = 200

2x = 200

$\implies x =\frac{200}{2}=100$

Hence, total profit = 20x = 20(100) = 2000 rupees,

OPTION d) is correct.

#Learn more:

A, B and C started a business with a total  investment of Rs.72000. A invests Rs. 6000  more than B and B invests Rs. 3000 less than C.  If the total profit at the end of a year Rs.8640,  find A's share​

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