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Manisha borrowed a total amount of Rs. 40000, part of it on simple interest rate of 16% per annum and remaining on simple interest rate of 12% per annum. If at the end of 3 years she paid in all Rs. 56320 to settle the loan amount, what was the amount borrowed at 16% per annum?1). Rs. 160002). Rs. 180003). Rs. 175004). Rs. 12000 |
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Answer» We know that, Interest = Amount - Principal Interest = 56320 - 40000 = Rs. 16320 Let’s assume the amount borrowed at rate of 16% per annum be X ⇒ Remaining amount = 40000 - X We know the formula for simple Interest, SI = (P × R × t)/100 Where, SI = Simple Interest P = Principal R = Rate of Interest t = TIME period Here Rate of interest is different for each part, so we can calculate SI for each part then we will add SI for each part to calculate total SI SI for first part of amount X, Rate of Interest = 16% ⇒ SI1 = (X × 16 × 3)/100 = 48X/100 SI for SECOND part of amount (40000 - X), Rate of Interest = 12% $(\Rightarrow {\rm{S}}{{\rm{I}}_2} = \frac{{\left( {40000 - {\rm{X}}} \right) \TIMES 12 \times 3}}{{100}} = \frac{{1440000}}{{100}} - \frac{{36X}}{{100}} = 14400 - \frac{{36X}}{{100}})$ Total Simple Interest = SI1 + SI2 = Rs. 16320 (as calculated above) ⇒ (48X/100) + 14400 - (36X/100) = 16320 ⇒ 12X/100 = 16320 - 14400 ⇒ X = 1920/0.12 = Rs. 16000 ∴ The amount borrowed at rate of 16% per annum = Rs. 16000 |
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