Question

the equal sums were invested for 5 years, the rate of interest being 10 per and 11 per p.a. If at the end of the period the total interest becomes rs 1155 the total amount inversted is ​

Answer 1

SOLUTION

GIVEN

• The equal sums were invested for 5 years, the rate of interest being 10 per and 11 per p.a.

• If at the end of the period the total interest becomes Rs 1155

TO DETERMINE

The total amount invested

EVALUATION

Let Rs P is invested in each investment

For first case

Principal = P

Time = t = 5 years

Rate of interest = r% = 10%

So the interest

$\displaystyle \sf{ = \frac{P \times 10 \times 5}{100} }$

$\displaystyle \sf{ = \frac{50P }{100} }$

For second case

Principal = P

Time = t = 5 years

Rate of interest = r% = 11%

So the interest

$\displaystyle \sf{ = \frac{P \times 11 \times 5}{100} }$

$\displaystyle \sf{ = \frac{55P }{100} }$

So by the given condition

$\displaystyle \sf{\frac{50P }{100} + \frac{55P }{100} = 1155 }$

$\displaystyle \sf{ \implies \: \frac{105P }{100} = 1155 }$

$\displaystyle \sf{ \implies \: P = 1155 \times \frac{100}{105} }$

$\displaystyle \sf{ \implies \: P = 1100 }$

Hence Rs 1100 is invested in each case

Hence the total investment

= Rs ( 2 × 1100 )

= Rs 2200

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