Aptitude - Partnership - Discussion

An easy way;

A = 7/2 * 4+ 7/2 * 3/2*8 = 14 + 42 = 56.
B = 4/3*12 = 16.
C = 6/5*12 = 14.4,
Total = 56 + 16 + 14.4 = 86.4
So, 86.4 = 21600,
Then B's Share 16 = 4000 (Ans)

A:B:C = 7/2:4/3:6/5.

Take lcm of 2,3,5 which will be 30
= 7 * 15 : 4 * 10 : 6 * 6,
=105x : 40x : 36.

A share for four months =105 * 4 = 420x.
A share after 8 months= 105 * 8 = 840x.
With 50 increase of total share.
If share is 100 then A share increases of 50 % = 100 + 50 = 150/100.
Therefore, A share for 8 months wth increased share = 840 * 150/100 = 1260.
A share for 12 months = 1260 + 420 = 1680x.
B share for 12 months = 40x * 12 = 480x.
C share for 12 months = 36x * 12 = 144x.

Ratio of A : B : C = 1680x : 480x : 144x
35x : 10x : 9x.
Total profit = 21600.
B share = 21600 * 10/54.
= 4000RS.

The question can be a bit misleading. It has to be specified that A's share increases without a reduction in the shares of B and C, with the total amount of investment increasing as a result. Without this clarification, it could well be that A's share increases at the expense of the others' shares and that the total level of investment remains the same.

Please explain the answer briefly.

Initially, A has Rs.105x investment for 4 months. After 4 months, he increased 50 percent of his Rs.105x(share) into a partnership for remaining months.So;

4 months =4*105x.
months (12-4) = 8 months = 8(105x+(50/100) * 105x).

(4*105x+8(105x+(50/100)*105x) : 12*40 : 12*36) = 1680:4800:432 = 35:10:9(when divided by 48).

Hence, B's share = Rs. 21600 * 10/(sum of 35,10,9) = Rs. 4000.

Why multiped and divided 15, 10, 6?

A = 7/2 = 15*7/15*2 = 105/30.
B = 4/3 = 10*4/10*3 = 40/30.
C = 6/5 = 6*6/5*6 = 36/30.

A's share of 4 month = 7/2 * 4 = 14.

A's share of 8 month = (50% of 7/2)*8 = 21/4*8 = 42.

A's share total 12 months = 14 +42 = 56.

B's share total 12 months = 4/3 *12 = 16.

C's share total 12 months = 6/5 *12 = 14.4.

Now,

B's profit = 21600*(16/86.4) = 4000.

The LCM of the denominators:

Step-1:
2,3,5=30 and multiply each term by 30
(7/2)*30 = 105, (4/3)*30 = 40, (6/5)*30 = 36
So, capital ratio = 105: 40: 36.

Step-2:
A initially invests 105 for the first 4 months + then increases it by 50%, means 50% of 105 i.e,.(50/100)*105 = 52.5.
So his new capital is 105 + 52.5 = 157.5 (this new amount is invested for the remaining 8 months).

First 4 months:
105×4=420

Next 8 months (after increase):
157.5×8=1260
Total = 420 +1260 = 1680

B invested ₹40 for 12 months:
40 × 12 = 480

C invested ₹36 for 12 months:
36 × 12 = 432

Now we have:
A:B:C = 1680:480:432
= 35 : 10 : 9.

Total profit = Rs. 21,600.
The ratio sum = 35+10+9 = 54 parts.
value of 1 part = 21600/54 = 400,
So B’s share is 10 * 400 = 4000.

105x*8 ?

Here we need to find A, (1year=12months) so after 4 months means remaining 8 months.

& Then multiple with 2 b/c in this 8 months 50% more.

@Anurag.

Thank for good explanation. Really helpful.