Multiple choice

3 containers having capacities in the ratio 5 : 6 : 2 contain mixture of sugar Type A and Type B such that the ratio of A to B in them is 2 : 4, 1 : 3 and 3 : 5 respectively. If all the three containers of sugar are emptied in a single container, what will be the ratio of sugar Type A to sugar Type B in the final mixture?

  1. 85 : 91

  2. 98 : 227

  3. 47 : 109

  4. 391 : 919

  5. 393 : 959
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total parts = 5+6+2 = 13. Container 1: 5 units, A:B = 2:4 (1:2) -> A=5/3, B=10/3. Container 2: 6 units, A:B = 1:3 -> A=6/4=1.5, B=4.5. Container 3: 2 units, A:B = 3:5 -> A=2*(3/8)=0.75, B=1.25. Total A = 5/3 + 1.5 + 0.75 = 1.66 + 2.25 = 3.916. Total B = 10/3 + 4.5 + 1.25 = 3.33 + 5.75 = 9.083. Ratio A:B = 3.916/9.083 = 47/109.

AI explanation

Assume the capacities of the containers are 5x, 6x, and 2x. The quantities of sugar Type A in the containers are 2/6 of 5x, 1/4 of 6x, and 3/8 of 2x, which totals 5x/3, 3x/2, and 3x/4 respectively. The quantities of sugar Type B are 4/6 of 5x, 3/4 of 6x, and 5/8 of 2x, which totals 10x/3, 9x/2, and 5x/4 respectively. Adding the Type A quantities gives 47x/4, and adding the Type B quantities gives 109x/4, making the final ratio of sugar Type A to sugar Type B 47 to 109.

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