Question

Simple interest on a certain sum for 2.5 years at 10% per annum is 18 less than​

Answer 1

Question:

Simple interest on a certain sum for 2.5 years at 10% per annum is 18 less than the simple interest on the same sum for 3.5 years at 8% per annum. Find the sum.

Answer:

The the Principal is Rs. 600.

Step-by-step explanation:

Given :

Time = 2.5 year and 3.5 years

Rate = 10% and 8%

SI for 2.5 years at 10% is 18 less than SI on 3.5 years at 8%

To find :

The sum

Solution :

Case I -

• Principal = P
• Rate = 10%
• Time = 2.5 years

⇒ SI = PRT/100

⇒ SI = (P × 10 × 2.5)/100

⇒ SI = 25P/100

$\rule{300}{1.5}$

Case II -

• Principal = P
• Rate = 8%
• Time = 3.5

⇒ SI = PRT/100

⇒ SI = (P × 8 × 3.5)/100

⇒ SI = 28P/100

$\rule{300}{1.5}$

According to the question,

SI for 2.5 years at 10% is 18 less than SI on 3.5 years at 8%

⇒ 28P/100 = (25P/100 + 18)

⇒ 28P/100 - 25P/100 = 18

⇒ 3P/100 = 18

⇒ 3P = 18 × 100

⇒ 3P = 1800

⇒ P = 1800/3

⇒ P = 600

Principal = Rs. 600

$\therefore$ The the Principal is Rs. 600.

Answer 2

Solution

Given :-

Simple interest ( S )

Principal = P

Rate = 8%

Time = 3.5 years

Simple interest ( S' )

Principal = P

Rate = 10%

Time = 2.5 years

S - S' = Rs. 18

______________________

${ \boxed{ \mathtt{S \: = \: \frac{prt}{100} }}}$

$\implies \: \frac{p \: .8.(3.5)}{100}$

${\boxed {\mathtt{\implies \: S \: = \: \frac{28}{100} }}}$

Now in 2nd Case :-

☆ Formula is same

$\implies \: S' \: = \: \frac{p.10(2.5)}{100}$

${ \boxed{ \mathtt{ \implies \: \frac{25}{100} }}}$

→ S - S' = 18

$\implies \: \frac{28p}{100} \: - \: \frac{25p}{100 } \: = \: 18$

$\implies \: \frac{3p}{100} \: = \: 18$

$\implies \: 3p \: = \: 1800$

$\implies \: p \: = \: \frac{1800}{3}$

${ \red{ \boxed{ \mathtt{ \purple{ \implies \: p \: = \: 600}}}}}$

So the required Principal amount is Rs 600