Person A started a business by investing Rs. 65,000. After a few months, B joined him by investing Rs. 50,000. Three months after the joining of B, C joined the two with an investment of Rs. 55,000. At the end of the year, A got 50% of profit as his share. For how many months did A alone finance the business?

Given:

Person A started a business by investing Rs. 65,000.

After a few months, B joined him by investing Rs. 50,000.

Three months after the joining of B, C joined the two with an investment of Rs. 55,000.

A got 50% of profit as his share.

Formula used:

Profit ratio = Investment1 × Time₁ : Investment₂ × Time₂ : ........... Investment_n × Time_n

Calculation:

Let B invest the amount after x months

A invest for 12 month

B invest for (12 - x)

​⇒ (12 - x) months

Three months after the joining of B, C joined the two with an investment of Rs. 55,000.

C invest for (12 - x - 3)

⇒ (9 - x)

Profit share = A : B : C

Profit share = 65,000 × 12 : 50,000 × (12 - x) : 55,000 × (9 - x)

⇒ 156 : 10(12 - x) : 11(9 - x)

A got 50% of profit as his share

⇒ 156/(156 + 120 - 10x + 99 - 11x) = 1/2

⇒ 312 = 375 - 21x

⇒ 21x = 63

⇒ x = 3 month 

∴ A alone finance the business for 3 month.