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A man takes a loan of some amount at some rate of simple interest. After three years, the loan amount is doubled and rate of interest is decreased by 2%. After next 5 years, if the total interest paid on the whole is Rs. 13,600, which is equal to the same when the first amount was taken for \(11 \frac 1 3\) years, then the loan taken initially is:

A man takes a loan of some amount at some rate of simple interest. After three years, the loan amount is doubled and rate of interest is decreased by 2%. After next 5 years, if the total interest paid on the whole is Rs. 13,600, which is equal to the same when the first amount was taken for \(11 \frac 1 3\) years, then the loan taken initially is: Correct Answer Rs. 10,000

Given:

Total sum of simple interest on the loan for 3 years at r% and Simple interest on double the amount for next 5 years at (r – 2)% is 13,600.

Simple interest for 34/3 years on initial loan and initial rate is 13,600

Formula Used:

Simple Interest = P × r × t/100

Where P → Principal amount

r → Rate of interest

t → Time

Calculation:

Simple interest on the loan for 3 years at r% + Simple interest on double the loan amount for next 5 years at (r – 2)% = 13,600

⇒ + = 13,600

⇒ 3 × P × r + 10 × P × r – 20 × P = 13,600 × 100

⇒ 13 × P × r – 20 × P = 13,60,000      ---- (1)
Simple interest for 34/3 years on initial loan and initial rate = 13,600

⇒ (P × r × 34)/(3 × 100) = 13,600

⇒ P × r = 1,20,000      ---- (2)

Put the value of eq. (2) in eq. (1)

⇒ 13 × 1,20,000 – 20 × P = 13,60,000

⇒ 20 × P = 15,60,000 – 13,60,000

⇒ P = 2,00,000/20

⇒ P = 10,000

∴ The initial loan amount is Rs. 10,000.

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