Mohan lent some amount of money at 9% simple interest and an equal amount of money at 10% simple interest each for two years. If his total interest was Rs. 760, what amount was lent in each case ?

Explanation:-

Let the amount invested = Rs. P
According to the questions,
$$\eqalign{ & \Leftrightarrow \frac{{{\text{P}} \times 9 \times {\text{2}}}}{{100}} + \frac{{{\text{P}} \times {\text{10}} \times {\text{2}}}}{{100}} = 760 \cr & \Leftrightarrow \frac{{\left( {18{\text{P + 20P}}} \right)}}{{100}} = 760 \cr & \Leftrightarrow 38{\text{P = 76000}} \cr & \Leftrightarrow {\text{P = 2000}} \cr}$$
Alternate
Total interest percent
$$\eqalign{ & {\text{ = }}\left( {9 \times 2} \right)\% + \left( {10 \times 2} \right)\% \cr & \Rightarrow 38\% = 760 \cr & \Rightarrow 100\% = 2000 \cr}$$
Hence required principal
= Rs. 2000