A man invested on simple interest, $\frac{1}{4}$ of his capital at 7% p.a., another $\frac{1}{4}$ of the capital at 8% p.a. and the remaining capital at 10% p.a. He earned Rs. 700 as interest in one year. Find his total capital invested.

Rs. 8000

Let the total capital = 16

He invested $\frac{1}{4}$ of his capital at 7% = 16 × \(\frac{1}{4}\) × \(\frac{7}{100}\) = 0.28

He invested other $\frac{1}{4}$ of the capital at 8% = 16 × \(\frac{1}{4}\) × \(\frac{8}{100}\) = 0.32

He invested remaining 16 - 4 - 4 = 8 of his capital at 10% = 8 × \(\frac{10}{100}\) = 0.8

Now according to the question,

Total interest = 0.28 + 0.32 + 0.8 = 1.4

1.4 = 700

1 = \(\frac{700}{1.4}\)

16 = \(\frac{700}{1.4}\) × 16 = 8000