Multiple choice

A sum of Rs. 570 is divided among 66 persons consisting of men, women and children. The ratio of the sums of the shares of all men, all women and all children is 5 : 6 : 8, but the individual shares of a man, woman and child are in ratio 1 : 3 : 2. Find the share of each one of them (in Rs.).

  1. M-7, W-15, C-12

  2. M-5, W-15, C-10

  3. M-10, W-9, C-8

  4. M-5, W-7, C-12

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let M, W, C be the number of men, women, and children. Total = 66. Total money = 570. Shares ratio 5:6:8 means total shares for groups are 5k, 6k, 8k. 5k+6k+8k = 570 => 19k = 570 => k=30. Total money for men = 150, women = 180, children = 240. Individual shares ratio 1:3:2 means M=x, W=3x, C=2x. Total people: 150/x + 180/3x + 240/2x = 66 => 150/x + 60/x + 120/x = 66 => 330/x = 66 => x=5. Individual shares: M=5, W=15, C=10.

AI explanation

Let the individual shares of a man, a woman and a child be 1x, 3x and 2x, and the number of men, women and children be M, W and C. The total shares are 5:6:8, so M(x) = 5, W(3x) = 6 and C(2x) = 8, meaning the number of men, women and children are 5/x, 2/x and 4/x. The total number of persons is 66, so (5/x) + (2/x) + (4/x) = 66, which simplifies to 11/x = 66, giving x = 1/6. The share of a man is 1 * (1/6) = Rs. 1/6, but calculating the actual money distributed (5 + 6 + 8 = 19 parts for 570) yields 1 part = 30, meaning the ratios of total money multiplied by x give x = 5; thus, the shares are Rs. 5, Rs. 15 and Rs. 10.

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