Question

A certain sum amounts to rs 15748 in 3 years at simple interest at r % p. a. The same sum amounts to rs 16510 at r+2 % p.a. simple interest in same time. What is the value of r?
a) 10%
b) 8%
c) 12%
d) 6 %​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

A certain sum amounts to Rs. 15748 in 3 years at simple interest at r % p. a. The same sum amounts to Rs. 16510 at ( r + 2)% p.a. simple interest in same time. The value of r

a) 10%

b) 8%

c) 12%

d) 6 %

EVALUATION

Let principal = Rs. P

Case : 1

Principal = Rs. P

Time = t = 3 years

Rate of interest = r%

Amount after 3 years = Rs. 15748

So by the given condition

$\displaystyle \sf{ P + \frac{P \times 3 \times r}{100} = 15748 }$

$\displaystyle \sf{ \implies P + \frac{3P r}{100} = 15748 \: \: \: \: - - - (1)}$

Case : 2

Principal = Rs. P

Time = t = 3 years

Rate of interest = (r +2)%

Amount after 3 years = Rs. 16510

So by the given condition

$\displaystyle \sf{ P + \frac{P \times 3 \times (r + 2)}{100} = 16510 }$

$\displaystyle \sf{ \implies P + \frac{3P( r + 2)}{100} = 16510}$

$\displaystyle \sf{ \implies P + \frac{3P r}{100} +\frac{6P}{100} = 16510}$

$\displaystyle \sf{ \implies 15748 +\frac{6P}{100} = 16510}$

$\displaystyle \sf{ \implies \frac{6P}{100} = 16510 -15748 }$

$\displaystyle \sf{ \implies \frac{6P}{100} = 762}$

$\displaystyle \sf{ \implies P= 762 \times \frac{100}{6} }$

$\displaystyle \sf{ \implies P= 12700 }$

From Equation 1 we get

$\displaystyle \sf{ P + \frac{3P r}{100} = 15748}$

$\displaystyle \sf{ \implies P \bigg(1+ \frac{3 r}{100} \bigg) = 15748}$

$\displaystyle \sf{ \implies 12700 \bigg(1+ \frac{3 r}{100} \bigg) = 15748}$

$\displaystyle \sf{ \implies \bigg(1+ \frac{3 r}{100} \bigg) = \frac{15748}{12700} }$

$\displaystyle \sf{ \implies \frac{3 r}{100} = \frac{15748}{12700} - 1}$

$\displaystyle \sf{ \implies \frac{3 r}{100} = \frac{15748 - 12700}{12700} }$

$\displaystyle \sf{ \implies \frac{3 r}{100} = \frac{3048}{12700} }$

$\displaystyle \sf{ \implies 3 r = \frac{3048}{127} }$

$\displaystyle \sf{ \implies 3 r = 24 }$

$\displaystyle \sf{ \implies r = 8 }$

Hence the value of r = 8

FINAL ANSWER

Hence the correct option is b) 8%

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