Question

# 2 men and 5 boys can finish a piece of work in 4 days,while 3 men and 6 boys can finish it in 3 days.Find the time taken by one man alone to finish the work and that taken by one boy alone to finish the work.

Solution

## let 1 men can finish the work in x days and 1 boy can finish the work in y days. then 1 man's 1 day work = 1/x and 1 boy's one day work = 1/y according to the question--- 2/x + 5/y = 1/4    ------ (1) 3/x + 6/y = 1/3    --------(2) put 1/x =  u and 1/y = v in eq, (1) and (2) 2u + 5v = 1/4  = 8u + 20 v = 1    ----------- (3) 3u+ 6v =1/3 = 9u + 18 v = 1     ------------(4) solving equation  3 and 4 multiply equation 3 with 9 and 4 with 8          9 (8u +20v =1)         8( 9u + 18v =1)  by multiplying we get  72u + 180v =9         ------ (5)  72u + 144v =8        -------(6) now subtract eq. 5 from 6         72u + 180v =9           72u + 144v =8            -          -          -    _______________________                    36V = 1         so v= 1/36  put v = 1/36 in eq. 3       8u + 20 X 1/36 = 1    8u =4/9         72u = 4      u = 1/18 u= 1/x = 1/18        x = 18 days   v = 1/y = 1/36       y = 36 days  so man can finish work in 18 days and boy can finsh work in 36 days MathematicsSecondary School Mathematics XStandard X

Suggest Corrections

0

Similar questions
View More

Same exercise questions
View More

People also searched for
View More