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The total sum of amounts of A and B at the end of 4 years and 2 years respectively on the same principal is Rs. 20,020. If A is charged Simple interest at the rate 10% and B is charged Compound interest at the rate 5%. The principal is?1. Rs. 5,0002. Rs. 7,5003. Rs. 2,5004. Rs. 8,0005. Rs. 6,000 |
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Answer» Correct Answer - Option 4 : Rs. 8,000 Given: The sum of amounts of A and B at the end of 4 years and 2 years respectively on the same principal = Rs. 20,020 Concept used: 1.) S.I. = (P × T × R)/100 2.) A = P + S.I. 3.) A = P(1 + R/100)T Where, S.I. → Simple interest A → Amount P → Principal T → Time R → Rate Calculations: Let the principal be x According to the question \(\Rightarrow {\rm{}}\left( {{\rm{x}} + {\rm{}}\frac{{{\rm{x\;}} \times {\rm{\;}}4{\rm{\;}} \times {\rm{\;}}10}}{{100{\rm{\;}}}}} \right){\rm{}} + {\rm{x}}{\left( {1{\rm{}} + {\rm{}}\frac{5}{{100}}} \right)^2}{\rm{}} = {\rm{}}20,020\) ⇒ 7x/5 + x(441/400) = 20,020 ⇒ (560x + 441x)/400 = 20,020 ⇒ 1001x/400 = 20,020 ⇒ x = 8000 ∴ The principal is Rs. 8,000 |
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