A man invests 1/3rd of his income at 7%, 1/4th at 8% and the remainder of his income at 10%.If the annual profit is Rs 561.What was the initial capital?Rs.7500Rs.6600Rs.4500Rs.3000
Question
A man invests 1/3rd of his income at 7%, 1/4th at 8% and the remainder of his income at 10%.If the annual profit is Rs 561.What was the initial capital?Rs.7500Rs.6600Rs.4500Rs.3000
Solution
To solve this problem, we need to set up an equation based on the information given.
Let's denote the man's total income as X.
According to the problem, he invests 1/3 of his income at 7%, 1/4 of his income at 8%, and the remainder at 10%.
So, the total annual profit from these investments is Rs 561.
We can express this as an equation:
(1/3)X0.07 + (1/4)X0.08 + (1 - 1/3 - 1/4)X0.10 = 561
Solving this equation will give us the value of X, which is the man's total income.
Let's simplify the equation:
0.07X/3 + 0.08X/4 + 0.10X*(5/12) = 561
Multiply through by 12 to get rid of the fractions:
0.074X + 0.083X + 0.105X = 56112
0.28X + 0.24X + 0.50X = 6732
Add the X terms together:
1.02X = 6732
Finally, solve for X by dividing both sides of the equation by 1.02:
X = 6732 / 1.02
X = Rs.6600
So, the man's initial capital was Rs.6600.
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