Multiple choice

A man lends $Rs. 350$ for $6$ years and $Rs. 540$ for $2\dfrac {1}{2}$ years to two person and receives in all $Rs. 85$ as interest. Find the rate per cent, if simple interest be reckoned

  1. $7$%
  2. $ \dfrac{170}{69}$%
  3. $3.33$%
  4. $3$%
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B Correct answer
Explanation

Simple interest formula: I = (P1*R*T1)/100 + (P2*R*T2)/100. 85 = (350*R*6)/100 + (540*R*2.5)/100. 85 = 21R + 13.5R = 34.5R. R = 85 / 34.5 = 170 / 69%.

AI explanation

Let the rate of interest be R% per annum, allowing us to use the combined simple interest formula: Total Interest = (P1*T1 + P2*T2) * R / 100. Substituting the given values gives 85 = (350*6 + 540*2.5) * R / 100. This simplifies to 85 = (2100 + 1350) * R / 100, which results in 85 = 34.5R, so R = 8500/345. By simplifying the fraction, R equals 170/69. The result is 170/69%.

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