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

GiVen:

• CI for 2nd year = Rs 880
• CI for 3rd year = Rs 968

So,

SI for Rs 880 per year = 968 - 880 = 88

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AnSwer:

★ Rate of interest = 88 × 100/ 880×1 = 10 %

Let original money be x.

Now,

★ Amt. after 2 years - Amt. after 1 year = CI for 2nd year.

$\sf \implies \: x {(1 + \dfrac{10}{100} )}^{2} - (1 + \dfrac{10}{100}) = 880 \\ \\ \sf \implies \: x\bigg \{ ({ \dfrac{11}{10} )}^{2} - \dfrac{11}{10}\bigg \} = 880 \\ \\ \sf \implies \: x \bigg \{ \frac{121}{100} - \dfrac{11}{10} \bigg \} = 880 \\ \\ \sf \implies \:x \times \dfrac{11}{100} = 880 \\ \\ \sf \implies \:x = 8000$

Therefore, rate of interest is 10 % and original money is Rs 8000.

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Answer 2

GivEn:-

• Compound Interest for 2nd year = Rs. 880

• Compound Interest for 3rd year = Rs. 968

To find:-

• Rate of interest and the original money.

SoluTion:-

$\therefore$ 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 -

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

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

$:\implies\sf \cancel{ \dfrac{8800}{880}} = R$

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

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Lets the original money be Rs. P

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

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

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

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

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

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

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

$:\implies\sf \cancel{ \dfrac{88000}{11}} = P$

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

$\therefore$ The rate of interest = 10% and,

$\therefore$ The original money = Rs. 8000.

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