Question

A man had Rupees 4000, part of which he lent at 5% and the rest at 4%. The whole interest received was Rupees 190.
How much did he lent at 4%?​

Answer 1

Answer:

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Step-by-step explanation:

Let us assume that,the sum lent at 5% = Rs. X

Then, amount at 4% = 4000 - X

According to the question,

$\frac{x\times 5 \times 1}{100} + \frac{(4000 - x)\times 4\times 1}{100} = 190 \\ \\ \frac{x\times 5\times 1 + (4000 - x)\times 4\times 1}{100} = 190 \\ \\ 5\times x + 16000 - 4\times x = 19000 \\ \\ x = 19000 - 16000 \\ \\ x = 3000$

He lent on 4% Rs. 3000/-

Answer 2

• AnswEr :

Let the First Part lent at 4% be Rs. n and, Second Part lent at 5% be Rs. (4000 – n).

$\bigstar\:\boxed{\sf Simple \:Interest = \dfrac{Principal \times Rate \times Time}{100}}$

$\underline{\bigstar\:\textsf{According to the Question Now :}}$

$\begin{gathered}:\implies\sf SI_1 + SI_2 = Total \:Interest\\\\\\:\implies\sf \dfrac{P_1R_1T}{100}+\dfrac{P_2R_2T}{100}=Rs.\:190 \\\\\\:\implies\sf \dfrac{n \times 4 \times 1}{100}+\dfrac{(4000 - n) \times 5 \times 1}{100}=Rs.\:190\\\\\\:\implies\sf \dfrac{4n}{100}+\dfrac{20000 - 5n}{100}=Rs.\:190\\\\\\:\implies\sf \dfrac{4n + 20000 - 5n}{100}=Rs.\:190\\\\\\:\implies\sf20000 - n = 190 \times 100\\\\\\:\implies\sf20000 - n = 19000\\\\\\:\implies\sf20000-19000 = n\\\\\\:\implies\boxed{\sf n = Rs. \:1000}\end{gathered}$

⠀

$\therefore\:\underline{\textsf{Money lent at 4\% wil be \textbf{Rs. 1000}}}$