Multiple choice

A sum of $Rs.\,5000$ was lent partly at $6\%$ and partly at $9\%$ simple interest. If the total interest received after $1$ year was $Rs.\,390$, what was the ratio in which the money was lent at $6\%$ and $9\%$?

  1. $1\,\colon\,5$.
  2. $2\,\colon\,5$.
  3. $2\,\colon\,3$.
  4. $1\,\colon\,3$.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be the amount at 6 percent and (5000-x) at 9 percent. 0.06x + 0.09(5000-x) = 390. 0.06x + 450 - 0.09x = 390. -0.03x = -60. x = 2000. The other part is 3000. Ratio = 2000:3000 = 2:3.

AI explanation

Let the first part be x, making the second part 5000 minus x. Setting up the simple interest equation for one year gives (x x 6 x 1)/100 + ((5000 minus x) x 9 x 1)/100 = 390. Multiplying by 100 and solving results in 6x + 45000 minus 9x = 39000, meaning 3x = 6000, so the first part x is Rs. 2000 and the second part is Rs. 3000. The ratio of these parts is 2:3.

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