Multiple choice

There are three bottles of mixture of syrup and water of ratios 2 : 3, 3 : 4 and 7 : 5. 10 litres of the first and 21 litres of the second bottle are taken. How much quantity from the third bottle is to be taken so that the final mixture from the three bottles will be of ratio 1 : 1?

  1. 25 litres

  2. 20 litres

  3. 35 litres

  4. 30 litres
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D Correct answer
Explanation

Let x be the quantity taken from the third bottle. Syrup/Water ratios are 2/5, 3/7, 7/12. Total syrup = 10*(2/5) + 21*(3/7) + x*(7/12) = 4 + 9 + 7x/12 = 13 + 7x/12. Total water = 10*(3/5) + 21*(4/7) + x*(5/12) = 6 + 12 + 5x/12 = 18 + 5x/12. Since the final ratio is 1:1, 13 + 7x/12 = 18 + 5x/12. Solving for x: 2x/12 = 5, so x/6 = 5, x = 30.

AI explanation

From 10 litres of the first mixture, syrup is 2/5 of 10, which is 4 litres, and water is 6 litres. From 21 litres of the second mixture, syrup is 3/7 of 21, which is 9 litres, and water is 12 litres. Let x litres be taken from the third bottle, so syrup is 7x/12 and water is 5x/12; setting the total syrup equal to total water gives 13 + 7x/12 = 18 + 5x/12. Solving this equation yields 2x/12 = 5, so x equals 30 litres.

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