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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 days2). 9/4 days3). 7/2 days4). 11/4 days |
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Answer» 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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