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CBSE Class 10 Answered

8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days. Find the time taken to finish the work by one man alone.
Asked by mkmishra101 | 21 Jun, 2016, 03:10: PM
Expert Answer
begin mathsize 12px style Let space the space time space taken space by space one space man space to space complete space the space work space be space straight x space and space time space taken space by space one space boy space to space complete space
the space work space be space straight y.
So comma space in space one space day space one space man space can space complete space 1 over straight x space part space of space the space work space and space one space boy space can space complete space 1 over straight y space part space of space the space work.
Since space 8 space men space and space 12 space boys space can space finish space straight a space piece space of space work space in space 10 space days comma
rightwards double arrow 8 over straight x plus 12 over straight y equals space 1 over 10 space and space 6 over straight x plus 8 over straight y equals space 1 over 14
Since space the space equations space are space not space linear comma space let space 1 over straight x equals space straight a space and space 1 over straight y equals straight b.
rightwards double arrow 8 straight a space plus space 12 straight b space equals space 1 over 10 space and space 6 straight a space plus space 8 straight b space equals space 1 over 14
Multiply space the space first space equation space by space 3 space and space the space second space equation space by space 4 comma space we space get
24 straight a space plus space 36 straight b space equals space 3 over 10 space and space 24 straight a space plus space 32 straight b space equals space 2 over 7
Subtract space the space equations space obtained.
24 straight a space plus space 36 straight b space minus 24 straight a space minus space 32 straight b equals space 3 over 10 minus 2 over 7
4 straight b equals 1 over 70 rightwards double arrow straight b equals 1 over 280
Substitute space in space equation space 8 straight a space plus space 12 straight b space equals space 1 over 10 space to space obtain space the space value space of space straight a.
8 straight a space plus space 12 open parentheses 1 over 280 close parentheses space equals space 1 over 10 rightwards double arrow straight a equals 1 over 140
So comma space straight x space equals 1 over straight a space equals 140 space and space straight y space equals 1 over straight b equals space 280
Hence comma space one space man space can space finish space the space work space in space 140 space days. end style
Answered by Rebecca Fernandes | 21 Jun, 2016, 04:21: PM
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