Seven men, five women and eight children were given an assignment of distributing 2000 books to students in a school over a period of three days. All of them distributed books on the first day. On the second day two women and three children remained abse

Seven men, five women and eight children were given an assignment of distributing 2000 books to students in a school over a period of three days. All of them distributed books on the first day. On the second day two women and three children remained absent and on the third day three men and five children remained absent. If the ratio of the number of books distributed in a day by a man, a woman and a child was 5: 4: 2 respectively, a total of ??approximately?? how many books were distributed on the second day ?
1). 1000
2). 800
3). 650
4). 900

Solution

Let the number of book distributed in a day by a man = 5x

woman = 4x & child = 2x

Day 1 : There were 7 men, 5 women, 8 children

=> No. of books sold = (7 * 5x) + (5 * 4x) + (8 * 2x)

= 35x + 20x + 16x = 71x

Day 2 : There were 7 men, 3 women, 5 children [As, 2 women & 3 children were absent]

=> No. of books sold = (7 * 5x) + (3 * 4x) + (5 * 2x)

= 35x + 12x + 10x = 57x

Day 3 : There were 4 men, 5 women, 3 children [As, 3 men & 5 children were absent]

=> No. of books sold = (4 * 5x) + (5 * 4x) + (3 * 2x)

= 20x + 20x + 6x = 46x

Now, total books distributed on the course of three days = 71x + 57x + 46x = 2000

=> x = 2000/174

No. of books distributed on the second day = 57x = 57 * $\frac{2000}{174}$ = 655.17 = ~650

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