Question

A sum is borrowed at $3.5\%$$p.a$ for $2years$. If an amount of $Rs7490$ was paid at the end of $2^{nd}$ $year$, then find the sum borrowed.

Answer 1

Given ,

Rate of Interest , $R\%$$=$$3.5\%$

Principal , $P$ $=$…………

Time , $T$ $=$$2years$

Amount, $A$$=$$Rs7490$

Note : $Amount=Principal+Interest$ or $A=P+I$

Here we have to find Interest $I$,

So, $I=A-P$

$I=7490-P$

Note : we have a formula to find $I$, when $R\%$, $P$, $T$ are given $I$$=$ $\frac{P\times T\times R}{100}$

Apply the formula ,

$I$$=$$\frac{P\times 2\times 3.5}{100}$

$I$$=$$\frac{P\times 7}{100}$

( on cross multiplication , we get )

$100\times I=P\times 7$

Substitute $I=7490-P$ in above equation,

$100\times (7490-P)=P\times 7$ ( apply distributive property over subtraction )

$749000-100P=7P$

transpose $\text{'}-100P\text{'}$ to the RHS

$749000=7P+100P$

$749000=107P$

Rewrite as ,

$107P=749000$ ( transpose $107$ to the RHS )

$P=\frac{749000}{107}$ ( divide $749000$ by $107$ , we get $7000$ )

$P=7000$

Therefore, the sum of money borrowed i.e Principal $P$ is $Rs7000$

Hence, the answer for the given blank is $Rs7000$ .