Question

the simple interest on a certain sum for 5 years at 8 percent per annum is Rs 120 more than the simple interest on the same for 3 years at 10 percent per annum find the sum​

Answer 1

Answer:

The required principle is Rs. 1200.

Step-by-step-explanation:

Let the principle be Rs. x.

For the first time simple interest on the principle,

• Principle ( P ) = Rs. x
• Rate of interest ( R ) = 8 %
• Time period ( N ) = 5 years

For the second time simple interest on the principle,

• Principle ( P ) = Rs. x
• Rate of interest ( R ) = 10 %
• Time period ( N ) = 3 years

From the given condition,

Simple interest for the first time = Simple interest for the second time + Rs. 120

$\displaystyle{\therefore\:\sf\:\dfrac{P\:\times\:R\:\times\:N}{100}\:=\:\dfrac{P\:\times\:R\:\times\:N}{100}\:+\:120}$

$\displaystyle{\implies\sf\:\dfrac{x\:\times\:8\:\times\:5}{100}\:=\:\dfrac{x\:\times\:10\:\times\:3}{100}\:+\:120}$

$\displaystyle{\implies\:\sf\:\dfrac{x\:\times\:40}{100}\:=\:\dfrac{x\:\times\:30}{100}\:+\:120}$

$\displaystyle{\implies\:\sf\:\dfrac{40\:x}{100}\:=\:\dfrac{30\:x}{100}\:+\:120}$

$\displaystyle{\implies\:\sf\:\dfrac{40\:x}{100}\:=\:\dfrac{30\:x\:+\:120\:\times\:100}{100}}$

$\displaystyle{\implies\:\sf\:\dfrac{40\:x}{\cancel{100}}\:=\:\dfrac{30\:x\:+\:12000}{\cancel{100}}}$

$\displaystyle{\implies\sf\:40\:x\:=\:30\:x\:+\:12000}$

$\displaystyle{\implies\sf\:40\:x\:-\:30\:x\:=\:12000}$

$\displaystyle{\implies\sf\:10\:x\:=\:12000}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{1200\cancel{0}}{\cancel{10}}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:x\:=\:Rs\:.\:1200}}}}$

∴ The required principle is Rs. 1200.