Person A started a business by investing ₹65,000. After a few months, B joined him by investing ₹50,000. Three months after the joining of B, C joined the two with an investment of ₹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?
Answer & explanation
Correct answer: option 2
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
⇒ \(\frac{156}{(156 + 120 - 10x + 99 - 11x)}\) = \(\frac{1}{2}\)
⇒ 312 = 375 - 21x
⇒ 21x = 63
⇒ x = 3 month