A sum of Rs. 1750 is divided into two parts such that the interests on the first part at 8% simple interest per annum and that on the other part at 6% simple interest per annum are equal. The interest on each part ( in Rupees) is ?

Answer: Option A

$$\begin{array}{rl}& \text{Principal = Rs}\text{. 1750}\\ & \text{Let the first part = }x\\ & \text{Hence second part}\\ & \text{ = }\left(1750-x\right)\\ & \text{According to the question,}\\ & \Rightarrow x\times \frac{8}{100}\times 1=\left(1750-x\right)\times \frac{6}{100}\times 1\\ & \Rightarrow 4x=5250-3x\\ & \Rightarrow 7x=5250\\ & \Rightarrow x=750\\ & \text{First part = Rs}\text{. 750}\\ & \therefore \text{ Second part}\\ & \text{ = Rs}\text{. }\left(1750-750\right)\\ & \text{ = Rs}\text{. 1000}\\ & \text{Required interest}\\ & \text{ = 750}\times \frac{8}{100}\\ & \text{ = Rs}\text{. 60}\end{array}$$

Alternate
Note : In such type of questions to save your valuable time follow the given below method.
Let, Principal = 100 units in both cases

		1st part		2nd part		Total
Principal	→	100×3	:	100×4	+→	700 units
Interest	→	8×3	:	6×4

Note : Interest is same in both cases
According to the question,
$$\begin{array}{rl}& \text{700 units = Rs}\text{. 1750}\\ & \text{1 unit = Rs}\text{. }\frac{1750}{700}\\ & \text{24 units = Rs}\text{. }\frac{1750}{700}\times 24\\ & =\text{Rs}\text{. 60}\\ & \text{Hence, required interest}\\ & \text{ = Rs}\text{. 60}\end{array}$$