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 ?

Solution(By Examveda Team)

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

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,
$$\eqalign{ & {\text{700 units = Rs}}{\text{. 1750}} \cr & {\text{1 unit = Rs}}{\text{. }}\frac{{1750}}{{700}} \cr & {\text{24 units = Rs}}{\text{. }}\frac{{1750}}{{700}} \times 24 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 60}} \cr & {\text{Hence, required interest}} \cr & {\text{ = Rs}}{\text{. 60}} \cr} $$