Question

14-Anil borrowed a sum of 12300 for a certain period at the rate of 10% period at the rate of 10% per annum and returned 18450 rs
on expiry of the time. Find the time for which money was borrowed by him.​

Answer 1

$\large{\red{\underline{ \: \: \sf Question: \: \: }}}$

Anil borrowed a sum of Rs12300 for a certain period at the rate of 10% per annum and returned Rs18450 on expiry of the time. Find the time for which money was borrowed by him.

$\Large{\green{\underline{ \: \: \: \sf Given: \: \: }}}$

• $\textsf{Principal, P = Rs12300}$
• $\textsf{Rate, R = 10 \%}$
• $\textsf{Amount = Rs18450}$

$\Large{\green{\underline{ \: \: \: \sf Find: \: \: }}}$

• $\textsf{Time, T = ?}$

$\Large{\green{\underline{ \: \: \: \sf Solution: \: \: }}}$

$\large{\red{\textsf{we, know that}}}$

$\boxed{\purple{\sf S.I. = Amount - Principal}}$

where,

• Amount = Rs18450
• Principal = Rs12300

So,

$\dashrightarrow\pink{\sf S.I. = Amount - Principal}$

$\dashrightarrow\pink{\sf S.I. =18450 - 12300}$

$\dashrightarrow\pink{\sf S.I. =6150}$

$\dashrightarrow\pink{\sf S.I. = Rs6150}$

$\therefore\green{\sf S.I. = Rs6150}$

$\Large{\blue{\textsf{we, know that}}}$

$\boxed{ \orange{\sf Simple \: Interest = \dfrac{P \times R \times T}{100} }}$

where,

• Simple Interest, S.I. = Rs6150
• Principal, P = Rs12300
• Rate, R = 10%

So,

$\looparrowright \purple{\sf Simple \: Interest = \dfrac{P \times R \times T}{100}}$

$\looparrowright \purple{\sf 6150 = \dfrac{12300 \times 10 \times T}{100}}$

$\looparrowright \purple{\sf 6150 \times 100 = 12300 \times 10 \times T}$

$\looparrowright \purple{\sf 615000 = 123000 \times T}$

$\looparrowright \purple{\sf \dfrac{615000}{123000}= T}$

$\looparrowright \purple{\sf 5yrs= T}$

$\therefore \purple{\sf Time = 5yrs}$

Hence, the Time for which Money was borrowed is 5yrs