Aptitude - Partnership - Discussion

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.

First find the ratio.

Which is 105:40:36?

They have given A's share increases after 4 months which means for first 4 months it remains same and the next 8 months (as there are 12 months in a year) it increases by 50%, so we need to calculate first for 4 months separately and the for next 8 months after increasing by 50%.

A's contribution for 4 months = 105 * 4 = 420.

A's contribution for remaining 8 months = 105 * 8 = 840.

As A's share increases in this 8 months, we need to calculate it,

840 + (840/2) = 840 + 420 = 1260.

50% increase means 840/2.

Finally for a year=420+1260=1680.

50% increase of 840.

So,

840 + (*820/2) = 820 + 420 = 1260.

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.

7/2 of A's share for 4 month , 7/2*4= 14. and the remaining (14+7/4+7/2)*8= 56.EXPlAIN his share 7/2 kept for 4 month in business that is 14 . and 50% he increses after 4 month that is 7/4 now his share = 7/2+7/4*8 =42 , now 14+42=56 same as for B that is 4/3*12=16 and for C 6/5*12=14.4 now ratio is 56:16:14.4 = 86.4 B's share 16/86.4*21600= 4000 ANSWER

@All.

In partnership, profits are shared at the end of the year but not at point of changes in ratios in case profits are to be distributed periodically the profits should be ascertained for same periods b cause profits Maybe high in first 4 months and finally adjusted to 21600 another issue all partners ratios together should be equal to 1 again the extra 50% share of A shall be contributed by B and C so as to equal to 1.

Total profit calculated for 1 year.

So 1 year = 12 month.

Partnership ratio 7/2:4/3:6/5, we need to expand this ratio.

i.e, 7/2:4/3:6/5.

In this we need to take 30 = 2*3*5 common factor based on which we need expand.

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.

Hence expand ratio = 105:40:36.

(105*4) + (105*150/100) *8) : (40*12) : (36*12).

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.

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.

A=(105*4months)+((105*8months)+50%(105*8months))
=420+(420+840)
=1680

B=40*12months
=480

C=36*12months
=432

now u devide the above values by 48(all 3 values r devided without any fraction value)then u will get 35:10:9....

then add all 3 shares 35+10+9=54

for B share=21600*(B share/total share)
=21600*(10/54)
=4000rs

Find the minimum number that will be divide 2,3 and 5 simultaneously.

That is known as LEAST COMMON DENOMINATOR.It will be 30.

Then 7*15/30,4*10/30,6*6/30. BUT 15,10,6 are by dividing(the given denominator 2,3,5 with LCM=30).

Then we can avoid the common denominator 30,and Finally we can get 105=15*7, 40= 4*10, and 36= 6*6.

Thank you Rocky.