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3 boys and 4 girls can do a piece of work in 4.5 days. Also, 9 boys and 6 girls can do the same work in 2 days. In how many days will 6 boys and 8 girls finish the same work?

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3 boys and 4 girls can do a piece of work in 4.5 days. Also, 9 boys and 6 girls can do the same work in 2 days. In how many days will 6 boys and 8 girls finish the same work?
1). 13/2 days
2). 9/4 days
3). 7/2 days
4). 11/4 days


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Answered by on | Votes 0 |

Let 1 boy’s 1 day work be ‘x’ and 1 girl’s 1 day work be ‘y’.

Hence, we have,

⇒ 3x + 4y = 1/(4.5)

⇒ 3x + 4y = 2/9           …(1)

Also,

⇒ 9x + 6y = 1/2               …(2)

Multiplying eq. (1) by 3 and subtracting from (2), we get,

⇒ 9x + 6y – 9x – 12y = 1/2– 2/3

⇒ – 6y = –1/6

⇒ y = 1/36

Substituting in (1),

⇒ x = 1/27

⇒ 6 boys and 8 girls 1 day work = 6(1/27) + 8(1/36) = 2/9 + 2/9 = 4/9

∴ 6 boys and 8 girls will finish the same piece of work in 9/4 days.

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