Multiple choice

A sum of Rs. $10000$ is lent partly at $8\%$ and remaining at $10\%$ per annum. If the yearly interest on the average is $9.2\%$, what are the two parts?

  1. Rs. $4000$ and Rs. $6000$
  2. Rs. $3000$ and Rs. $7000$
  3. Rs. $2000$ and Rs. $8000$
  4. Rs.$1000$ and Rs. $8000$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x be invested at 8%, so 10000 - x is invested at 10%. The weighted average equation 0.08x + 0.10(10000 - x) = 920 gives x = Rs. 4000, leaving Rs. 6000.

AI explanation

Using the alligation method on the interest rates, we compare 8% and 10% against the average of 9.2%. This gives a ratio of (10 minus 9.2) to (9.2 minus 8), which equals 0.8 to 1.2 or 2 to 3. Dividing the total sum of Rs. 10000 in this 2:3 ratio, the two parts are (2/5) x 10000 = Rs. 4000 and (3/5) x 10000 = Rs. 6000.

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