Question

The compound interest, calculated yearly on a certain sum of money for the 2nd year is Rs 880 & for the 3rd year it is Rs 968. Calculate the rate of interest & the original money.​

Answer 1

Answer:

∵ Difference between the C.I of two successive years=Rs.880−968=Rs.88

∴Rate of interest=  

P×T

100×I

​  

=  

880×1

100×88

​  

=10%

Let the sum of money=Rs.100

∴interest for one year=10% of 100=  

100

10

​  

×100=Rs.10

Amount after one year=100+10=Rs.110

∴Interest foe second year=10% of 110=  

100

10

​  

×110=Rs.11

When the interest for second  year is rs .11 then sum=Rs.100

When the interest for second year is Rs.880 then sum=  

11

100

​  

×880=Rs.8000

Explanation:

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Answer 2

$\text{\large\underline{\red{Given:-}}}$

• Compound Interest for 2nd year = Rs. 880

• Compound Interest for 3rd year = Rs. 968

$\text{\large\underline{\green{To find:-}}}$

Rate of interest and the original money.

$\text{\large\underline{\purple{Solution:-}}}$

∴ S.I. on Rs. 880 for one year = Rs. 968 - Rs. 880 = Rs. 88

As we know that,

$\dag\;{\underline{\boxed{\bf{\red{S.I. = \dfrac{P \times R \times T}{100}}}}}}$

Now, Substituting values in above formula -

$\implies\sf 88 = \dfrac{880 \times R \times 1}{100}$

$\implies\sf \dfrac{88 \times 100}{880 \times 1}$

$\implies\sf \cancel{ \dfrac{8800}{880}}$

$\implies {\underline{\bf{\blue{R = 10 \%}}}}$

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Lets the original money be Rs. P

✠ C.I. for second year = Amount after 2 years - Amount after 1 year

$\implies\sf 880 = P \bigg( 1 + \dfrac{10}{100} \bigg)^2 - P \bigg( 1 + \dfrac{10}{100} \bigg)$

$\implies\sf 880 = P \bigg[ \bigg( \dfrac{11}{10} \bigg)^2 - \dfrac{11}{10} \bigg]$

$\implies\sf 880 = P \bigg( \dfrac{121}{100} - \dfrac{11}{10} \bigg)$

$\implies\sf 880 = P \times \dfrac{11}{100}$

$\implies\sf 880 \times 100 = P \times 11:$

$\implies\sf 88000 = P \times 11:$

$\implies\sf \cancel{ \dfrac{88000}{11}}$

$\implies {\underline{\bf{\blue{P = 8000}}}}$

∴ The rate of interest = 10% and,

∴ The original money = Rs. 8000.

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$\begin{gathered}\boxed{\begin{minipage}{7 cm}\boxed{\underline{\underline{\bigstar\:\bf\:Extra\:Brainly\:knowlegde\:\bigstar}}}\\\\1) Profit = SP - CP\\\\2) Loss = CP - SP\\\\3) Profit\% = (Profit in Rs.)*100/CP\\\\4) Loss\% = (Loss in Rs.)*100/CP\\\\5) SP = CP*(100+P\%)/100\\\\6) SP = CP*(100-L\%)/100\\\\7) CP = SP*100/(100+P\%)\\\\8) CP = SP*100/(100-L\%)\\\\9) Discount =MP - SP\\\\10) Discount\%=(Discount in Rs.)*100/MP\\\\11) SP = MP*(100-D\%)/100\\\\12) MP = SP*100/(100-D\%)\\\\\end{minipage}}\end{gathered}$

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