Study the information carefully and answer the questions that follow.
A, B and C started a business by investing Rs. 800, Rs. 1600 and Rs. 2000 respectively. In the second quarter, they invested amounts in the ratio 1 : 4 : 2. In the next quarter again, they invested amounts in the ratio 3 : 2 : 3. In the last quarter, the ratio of their investments were same as in the 2nd quarter. Also, in the last quarter, the respective amounts of A, B and C was double than the respective amounts invested in `2^(nd)` quarter. The total investment of C before `4^(th)` quarter was Rs 1400 more than that of A during the same duration. Also, ratio of B’s share in profit to total profit at the end of year was 66 : 153. Please note: All the investments were for one quarter only.
Find the total investment of A, B and C .

Options

A. Rs 10,200
B. Rs 11,300
C. Rs 9,800
D. Rs 10,080

Answer

A

Explanation

Quarters mean 3 months each
Ratio of investments in `2^(nd)` quarter for A, B, C is in the ratio 1 : 4 : 2, so let amounts be Rs. x, Rs. 4x and Rs. 2x respectively.
Ratio of investments in `3^(rd)` quarter for A, B, C is in the ratio 3 : 2 : 3, so let amounts be Rs. 3y, Rs. 2y, Rs. 3y respectively.
In the last quarter, investments of A, B, C are double of that in the `2^(nd)` quarter, so amounts would be Rs. 2x, Rs. 8x, Rs. 4x respectively.
Given: (2000 + 2x + 3y) = 1400 + (800 + x + 3y)
`rArr` x = 200
Now ratio of profit share of A : B : C is
`800 xx3+ x xx 3 + 3y xx 3 + 2xx x 3` :
`1600 xx 3+4x xx 3+ 2y xx 3 + 8x xx 3 : 2000 xx 3 + 2x xx 3 + 3y xx 3 + 4x xx 3`
`rArr` (800 + 3x +3y) : (1600 + 12x + 2y) : (2000 + 6x + 3y)
After putting x = 200, we get 1400 + 3y : 4000 + 2y : 3200 + 3y
ATQ,
`(4000+2y)/(1400+3y+4000+2y+3200 +3y)=66/153`
`rArr (2000+y)/(4300+4y)=22/51`
`rArr` y=200
So now the total investment = (800 + 3x + 3y) + (1600 + 12x + 2y) + (2000 + 6x + 3y) = (4400 + 21x + 8y)
After putting x = 200 and y = 200, total investment = Rs 10,200