Multiple choice

A sum of Rs $1550$ was lent partly at $5 $% p.a. and partly at $8$% p.a. simple interest. The total interest received after $3$ years is Rs $ 300$. What is the ratio of the money lent at $5$% to that at $8$% ?

  1. $12 : 13$
  2. $11 : 13$
  3. $16 : 15$
  4. $19 : 15$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be the amount at 5% and (1550 - x) be the amount at 8%. Interest = (x * 0.05 * 3) + ((1550 - x) * 0.08 * 3) = 300. 0.15x + 372 - 0.24x = 300. -0.09x = -72. x = 800. The amount at 8% is 1550 - 800 = 750. Ratio 800:750 = 16:15.

AI explanation

The total interest for 3 years on Rs 1550 is Rs 300, so the interest for 1 year is Rs 100. If Rs x is lent at 5%, then Rs (1550 - x) is lent at 8%, which gives the equation (5x/100) + 8(1550 - x)/100 = 100. Multiplying by 100 gives 5x + 12400 - 8x = 10000, meaning 3x = 2400 and x = 800. The two parts are Rs 800 and Rs 750, making the required ratio 16 : 15.

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