Find the total investment of A B and C ........

Quantitative Aptitude ( Phase -I) Partnership

Directions : A, B and C started a business by investing Rs 800, Rs 1600 and Rs 2000 respectively. After a quarter they invested amounts in a ratio 1 : 4 : 2. After another quarter, they invested amounts in ratio 3 : 2 : 3.In the last quarter the ratio of investments was same as in 2^nd 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 same duration. Also ratio of B’s share in profit to total profit at the end of year was 66 : 153.

Find the total investment of A, B and C.

Rs 10,200

Rs 11,300

Rs 9,800

Rs 10,080

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Explanation:

Quarters means 3 months each
Ratio of investments in 2^nd quarter – 1 : 4 : 2, so let amounts – x, 4x, 2x
Ratio of investments in 3^rd quarter – 3 : 2 : 3, so let amounts – 3y, 2y, 3y
In last quarter, respective amount is double then in 2^nd quarter, so amounts – 2x, 8x, 4x
In the last quarter the ratio of investments was same as in 2^nd quarter. — this is not required to solve question.
Given:
(2000 + 2x + 3y) = 1400 + (800+x+3y)
Solve, x = Rs 200
Now ratio of profit share —A : B : C is
800*3 + x*3 + 3y*3 + 2x*3 : 1600*3 + 4x*3 + 2y*3 + 8x*3 : 2000*3 + 2x*3 + 3y*3 + 4x*3
3 gets cancelled, gives
(800+3x+3y) : (1600+12x+2y) : (2000+6x+3y)
Put x = 200 gives
1400+3y : 4000+2y : 3200+3y
Now given
(4000+2y)/(1400+3y + 4000+2y + 3200+3y) = 66/153
(2000+y)/(4300+4y) = 22/51
Solve, y = Rs 200
So now the total investment is—(800+3x+3y) + (1600+12x+2y) + (2000+6x+3y) = (4400 + 21x + 8y)
put x = 200, y = 200, total investment = Rs 10,200