Question

Nidhi received simple interest of ₹1,200 when invested ₹ x at 6% p.a. and ₹ y at 5% p.a. for 1 year. Had she invested ₹ x at 3% p.a. and ₹ y at 8% p.a. for that year, she would have received simple interest of ₹1,260. Find the values of x and y.

Answer 1

SI on ₹ x at 6% p.a for 1 year

\( = \frac{₹(x\times 6\times1)}{100}\) 

\(= \ \frac{₹6x}{100} = \frac{₹3x}{50}\) 

SI on ₹y at 5% p.a. for 1 year 

\(= \frac{₹(y\times5\times1)}{100}\)  

\(= \frac{₹5y}{100} = \frac{₹1}{20} y\)  

Total SI = ₹1200   

\(\frac{3x}{50} + \frac{y}{20} = 1200\)  

⇒  \(\frac{6x+5y}{100} = 1200\)  

⇒  6x + 5y = 120000 …(1)  

SI on ₹x at 3% p.a. \(= ₹ \frac{(x\times3\times 1)}{100}\)

\(= ₹ \frac{3x}{100}\) 

S.I. on ₹ y at 8% p.a \(= \frac{₹(y\times8\times1)}{100} = ₹ \frac{2}{25} y\)  

\(\frac{3x}{100} + \frac{2y}{25} = 1260\)  

⇒  \(\frac{3x+8y}{100} = 1260\)  

⇒ 3x + 8y = 126000 …(ii)

Multiply equation (ii) by 2 and then subtract it from equation (i)