Question

Johnny and have to do with it​

Answer 1

Question:

Divide Rs. 8000 into two parts such that the SI on the first part of 5 years at 12 % per annum is equal to SI on the second part for 2 years at 18 % per annum.

Answer:

The two parts of the principle are Rs. 3000 & Rs. 5000.

Step-by-step-explanation:

Let the first part of the principle be Rs. x.

And the second part of the principle be Rs. y.

From the first condition,

x + y = 8000

⇒ x = 8000 - y

⇒ x = - y + 8000 $\displaystyle{\quad\:-\:-\:-\:-\:(\:1\:)}$

Now, we know that,

$\displaystyle{\pink{\sf\:Simple\:Interest\:=\:\dfrac{P\:\times\:R\:\times\:N}{100}}}$

For the simple interest on first part of the principle,

• Principle ( P ) = x
• Rate of interest ( R ) = 12 %
• Time period ( N ) = 5 years

For the simple interest on second part of principle,

• Principle ( P ) = y
• Rate of interest ( R ) = 18 %
• Time period ( N ) = 2 years

From the second condition,

$\displaystyle{\sf\:\dfrac{x\:\times\:12\:\times\:5}{\cancel{100}}\:=\:\dfrac{y\:\times\:18\:\times\:2}{\cancel{100}}}$

$\displaystyle{\implies\sf\:x\:\times\:12\:\times\:5\:=\:y\:\times\:18\:\times\:2}$

$\displaystyle{\implies\sf\:(\:-\:y\:+\:8000\:)\:\times\:12\:\times\:5\:=\:y\:\times\:18\:\times\:2\:\quad\:\:-\:-\:-\:[\:From\:(\:1\:)\:]}$

$\displaystyle{\implies\sf\:(\:-\:y\:+\:8000\:)\:\times\:60\:=\:y\:\times\:36}$

$\displaystyle{\implies\sf\:-\:60\:y\:+\:480000\:=\:36\:y}$

$\displaystyle{\implies\sf\:480000\:=\:36\:y\:+\:60\:y}$

$\displaystyle{\implies\sf\:96\:y\:=\:480000}$

$\displaystyle{\implies\sf\:y\:=\:\cancel{\dfrac{480000}{96}}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:y\:=\:Rs\:.\:5000}}}}$

By substituting y = 5000 in equation ( 1 ), we get,

x = - y + 8000 $\displaystyle{\quad\:-\:-\:-\:-\:(\:1\:)}$

⇒ x = - 5000 + 8000

⇒ x = 8000 - 5000

$\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:x\:=\:Rs\:.\:3000}}}}$

∴ The two parts of the principle are Rs. 3000 & Rs. 5000.