A man invests ₹6750, partly in shares of 6% at ₹140 and partly in shares of 5% at ₹125. If his total income is ₹280, how much has he invested in each ?

Let the investment of the man in shares of 6% at ₹140 be ₹x, then his investment in shares of 5% at ₹125 = ₹(6750 - x)

$\text{Income on 1 share of ₹140} = 6\% \text{ of ₹100} = ₹6 \\[0.5em] \text{Income on ₹x} = ₹\dfrac{6}{140}x = ₹\dfrac{3}{70}x \\[0.5em] \text{Income on 1 share of ₹125} = 5\% \text{ of ₹100} = ₹5 \\[0.5em] \text{Income on ₹(6750 - x)} = ₹\dfrac{5}{125}(6750 - x) = ₹\dfrac{1}{25}(6750 - x) \\[0.5em]$

But the total income of the man is ₹280,

$\therefore \dfrac{3}{70}x + \dfrac{1}{25}(6750 - x) = 280 \\[0.5em] \Rightarrow \dfrac{3}{70}x + \dfrac{1}{25}(6750 - x) = 280 \\[0.5em] \Rightarrow \dfrac{15x + 94500 - 14x}{350} = 280 \\[0.5em] \Rightarrow x + 94500 = 280 \times 350 \\[0.5em] \Rightarrow x = 98000 - 94500 \\[0.5em] \Rightarrow x = 3500 \\[0.5em] \therefore 6750 - x = 6750 - 3500 = 3250$

∴ Investment in 6% shares at ₹140 = ₹3500
and Investment in 5% shares at ₹125 = ₹3250