Question

A certain sum of money was invested at simple rate of interest for 3 years.If it was invested at 7% higher, the interest have been Rs. 882 more, then sum has been invested at that rate was

Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

case ❶ :-

→ Principal = let P .

→ Rate % = Let R.

→ Time = 3 Years.

→ SI = (P * R * T)/100 = (P * R * 3)/100 ------ Eqn(1)

Case ❷ :-

→ → Principal = let P .

→ Rate % = (R+7).

→ Time = 3 Years.

→ SI = (P * R * T)/100 = {P * (R+7) * 3}/100 ------ Eqn(2)

A/q,

→ 3P(R+7)/100 - (3PR)/100 = 882 ---------- Eqn(3)

→ (3PR+21P) - (3PR) = 88200

→ 21P = 88200

→ P = Rs.4200 (Ans.)

Hence, The sum invested was Rs.4200 .

_________________________

Shortcut :-

it is given that, due to Increase in Rate 7% we get Rs.882 More in 3 Years.

Hence, we can conclude That,

☛ (7*3)% -------------- Rs.882

☛ 100%(P) ----------- Rs.4200 (Ans.)

_________________________

Answer 2

${ \red { \bold{ \huge{ \underline{Question}}}}}$

▪ A certain sum of money was invested at simple interest for 3 years. If it was invested at 7% higher, the interest have Been Rs. 882 more, then the sum has been invested at that rate was??

${ \red{ \bold{ \huge{ \underline{ \: Solution}}}}}$

${ \boxed { \bold{ S.I.= \frac{P\times R \times T}{100} }}}$

where,

▪S.I. = simple interest

▪P = principal = the sum of money invested

▪R = the rate at which the sum has been invested

▪ T = time

¤ let the sum of money that was invested be Rs. P and the rate at which it is invested be x%

time = 3 years

therefore,

${ \bold{ \implies{S.I. \: at \: x = \frac{P\times x \times 3 }{100} }}}$

■ according to the question ,

if the sum was invested at 7% higher rate , then the interest have Been Rs. 882 more

here, R = rate = (x+7)%

Then, simple interest for (x+7)% ....

${ \bold{ \implies{S.I. \: at \: (x + 7) = \: \frac{P \times (x + 7) \times 3}{100} }}}$

it's given in the question that,

S.I. at (x+7)% = S.I. at x% + Rs.882



${ \bold {\implies{ \frac{3P(x + 7)}{100} = \frac{3Px}{100} + 882}}}$



${ \bold {\implies{ \frac{(3Px + 21P)}{100} = \frac{3Px}{100} + 882}}}$



${ \bold {\implies{ \frac{(3Px + 21P)}{100} - \frac{3Px}{100} = 882}}}$


${\bold {\implies{ \frac{3Px + 21P- 3Px}{100} = 882}}}$



${\bold{ \implies{ \frac{21P}{100} = 882}}}$



${\boxed{ \bold{ \implies{P = 4200}}}}$



the sum of money that was invesTed = Rs.4200