Multiple choice

A sum of Rs 1,200 was lent partly at 5% and partly 6% simple interest. The total interest received after 2 years was Rs 128. The ratio of the money lent out at 5% and 6% is

  1. 5:6

  2. 6:5

  3. 2:1

  4. 1:2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be amount at 5% and y be amount at 6%. x + y = 1200. Interest = (x * 0.05 * 2) + (y * 0.06 * 2) = 128. 0.1x + 0.12y = 128. Multiply by 100: 10x + 12y = 12800. Substitute x = 1200 - y: 10(1200-y) + 12y = 12800 => 12000 - 10y + 12y = 12800 => 2y = 800 => y = 400. Then x = 800. Ratio x:y = 800:400 = 2:1.

AI explanation

Using the alligation method, the overall interest rate for one year is 128 divided by (1200 times 2), which equals 128 divided by 2400, or 16 over 3 percent. Placing 16 over 3 between 5 percent and 6 percent, we find the ratio of the differences is (6 minus 16 over 3) to (16 over 3 minus 5). Calculating these gives 2 over 3 and 1 over 3, which establishes a ratio of 2 to 1 for the money lent at 5 percent to 6 percent.

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