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
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.