Correct option is D
Information Given:
A invested Rs. 2000.
B invested Rs. 6000.
A invested for 2 months more than B.
Total profit = Rs. 6600.
A’s profit share = Rs. 1800.
Asked: How many months did A invest?
Concept/Formula Used:
Profit ratio is proportional to investment × time.
A's investment × time : B's investment × time = A’s profit : B’s profit
Total profit = A’s profit + B’s profit
Explanation:
Let B invest for x months.
Then A invested for x + 2 months.
Investment × time for A = 2000 × (x + 2)
Investment × time for B = 6000 × x
A’s profit share is Rs. 1800 out of Rs. 6600,
So, profit ratio A : B = 1800 : (6600 - 1800) = 1800 : 4800 = 3 : 8
Set ratio of investments equal to profit ratio:
2000 × (x + 2) / (6000 × x) = 3 / 8
Cross multiply:
8 × 2000 × (x + 2) = 3 × 6000 × x
Simplify:
16000 (x + 2) = 18000 x
Expand left:
16000 x + 32000 = 18000 x
Bring terms to one side:
32000 = 18000 x - 16000 x = 2000 x
Solve for x:
x = 32000 / 2000 = 16
A’s investment duration = x + 2 = 16 + 2 = 18 months.
English
190 Questions
200 Marks
160 Mins
