3 men and 4 women can finish a work in 12 days whereas 5 men and 4 women can complete the same work in 9 days . Find the ratio between the amount of work done by a man to a woman .

Asked by Sanjay | 26th Mar, 2017, 11:11: AM

Expert Answer:

begin mathsize 12px style The space straight a space man space do space straight x space units space in space one space day space and space straight a space woman space do space straight y space units space in space one space day.
Since space 3 space men space and space 4 space women space can space finish space the space work space in space 12 space days comma
so comma space 3 space men space and space 4 space women space can space finish space 1 over 12 th space part space of space the space work space in space 1 space day.
rightwards double arrow 3 straight x plus 4 straight y equals 1 over 12 space.... left parenthesis straight i right parenthesis
Since space 5 space men space and space 4 space women space can space finish space the space work space in space 9 space days comma
so comma space 5 space men space and space 4 space women space can space finish space 1 over 9 th space part space of space the space work space in space 1 space day.
rightwards double arrow 5 straight x plus 4 straight y equals 1 over 9 space.... left parenthesis ii right parenthesis
Subtracting space equation space left parenthesis straight i right parenthesis space from space left parenthesis ii right parenthesis comma space we space get
2 straight x equals 1 over 9 minus 1 over 12
rightwards double arrow 2 straight x equals fraction numerator 4 minus 3 over denominator 36 end fraction
rightwards double arrow 2 straight x equals 1 over 36 rightwards double arrow straight x equals 1 over 72
Substituting space in space left parenthesis straight i right parenthesis comma space we space get
3 open parentheses 1 over 72 close parentheses plus 4 straight y equals 1 over 12
rightwards double arrow 1 over 24 plus 4 straight y equals 1 over 12
rightwards double arrow 4 straight y equals 1 over 12 minus 1 over 24
rightwards double arrow 4 straight y equals fraction numerator 2 minus 1 over denominator 24 end fraction
rightwards double arrow 4 straight y equals 1 over 24
rightwards double arrow straight y equals 1 over 96
Since space straight x equals 1 over 72 space and space straight y equals 1 over 96 comma space
so comma space the space ratio space between space the space amount space of space work space done space by space straight a space man space and space woman space equals space fraction numerator 1 over 72 over denominator 1 over 96 end fraction equals 4 over 3 comma space that space is space 4 space colon space 3. end style

Answered by Rebecca Fernandes | 26th Mar, 2017, 10:38: PM