Question

three persons a b,and c invest in a business in the ratio 5:6:4 if a and c invested for one year then b should invest for how many months if he wants to receive 25% of the total profit at the end of one year​

Answer 1

Answer:-

Given:-

Ratio of capitals of a, b & c = 5 : 6 : 4

Let us assume that b invests money for x months

So,

⟹ Ratio of their shares = 5 × 12 months : 6 × x months : 4 × 12 months.

[ 12 months are multiplied because a & c invested the money for 1 year ]

⟹ Ratio of their shares = 60 : 6x : 48 = 10 : x : 8

Now,

Let the profit received by all the three be Rs. P.

So,

⟹ B's share = 25% of P

⟹ { x/(10 + x + 8) } * P = (25/100) * P

⟹ x/(18 + x) = 25/100

⟹ 100x = 25(18 + x)

⟹ 100x/25 = 18 + x

⟹ 4x - x = 18

⟹ 3x = 18

⟹ x = 18/3

⟹ x = 6

∴ b invests money for 6 months.

Answer 2

Given :-

Three persons a b,and c invest in a business in the ratio 5:6:4 if a and c invested for one year then b should invest for how many months if he wants to receive 25%

To Find :-

Investment be x

Solution :-

Let the investment of b be x

Share of A = 5 × 12 = 60

Share of B = 6 × x = 6x

Share of C = 4 × 12 = 48

Ratio = 60:6x:48

Ratio = 30:3x:24

Ratio = 10:x:8

So,

Share of B = x/Ratio × Profit = 25% of profit

x/(10 + x + 8) × P = 25/100 × P

x/(18 + x) × P = 25/100 × P

x/(18 + x) = 25/100

100x = 25(18 + x)

100x = 450 + 25x

100x - 25x = 450

75x = 450

450/75 = x

6 = x