Question

P and Q invested in a business in the ratio 5:13. Q withdrew his capital after 6 months. if they shared thir profit in the ratio 25:26 for how long was P's amount used?​

Answer 1

Answer:

P’s amount was invested for 15 months. Since Q withdrew his capital after 6 months therefore, we can say that P had invested for 9 months more alone.

Step-by-step explanation:

Given data:  

Investment of P and Q is in the ratio of 5:13.  

Time period for Q’s investment, Tq = 6 months

Profit shared in the ratio, Pp/Pq = 25:26

Now let us take few assumptions:

Investment of P, Ip = 5y

Investment of Q, Iq = 13y

Since Q withdraws his capital after 6 months which means Q invested only for 6 months. Let the rest of time period that P’s investment was used be “x”. Therefore, P had invested for total time period of “Tp” = (x+6) months.

We know,

Profit = Investment * Time

∴ (Pp/Pq) = [ {Ip * Tp} / {Iq * Tq}]

Or, (25 / 26) = [ {5y * (x + 6)} / {13y * 6}]

Or, (25 / 26 ) = [ {5(x+6)} / {13 * 6} ]

Solving the equation, we get

Or, x + 6 = 5 * 3  

Or, x = 15 – 6

Or, x= 9

∴ P’s amount was used for a total time period of, Tp = x + 6 = 9 + 6 = 15 months.

Answer 2

Answer:

Step-by-step explanation:

P’s amount was invested for 15 months. Since Q withdrew his capital after 6 months therefore, we can say that P had invested for 9 months more alone.

Step-by-step explanation:

Given data:  

Investment of P and Q is in the ratio of 5:13.  

Time period for Q’s investment, Tq = 6 months

Profit shared in the ratio, Pp/Pq = 25:26

Now let us take few assumptions:

Investment of P, Ip = 5y

Investment of Q, Iq = 13y

Since Q withdraws his capital after 6 months which means Q invested only for 6 months. Let the rest of time period that P’s investment was used be “x”. Therefore, P had invested for total time period of “Tp” = (x+6) months.

We know,

Profit = Investment * Time

∴ (Pp/Pq) = [ {Ip * Tp} / {Iq * Tq}]

Or, (25 / 26) = [ {5y * (x + 6)} / {13y * 6}]

Or, (25 / 26 ) = [ {5(x+6)} / {13 * 6} ]

Solving the equation, we get

Or, x + 6 = 5 * 3  

Or, x = 15 – 6

Or, x= 9

∴ P’s amount was used for a total time period of, Tp = x + 6 = 9 + 6 = 15 months.