Question

X Y and Z together can do a piece of work in 4 days. If X and Y can do the work in
5 days. Y and Z in 10 days, find the number of days in which X and Z. while working
together, will be able to finish the work.
​

Answer 1

Answer:

x and z can finish the work in 5 days

Step-by-step explanation:

=)(x+y+z)'s 1 day work=1/4

=)z's 1 day work=(x+y+z)'s 1 day work - (x+y)'s 1 day work

                         =(1/4)-(1/5)

                         =(5-4)/20                                        [By taking L.C.M]

                         =1/20

=)x's 1 day work=(x+y+z)'s 1 day work-(y+z)'s 1 day work

                          =(1/4)-(1/10)

                          =(5-2)/20                                        [By taking L.C.M]

                          =3/20

=)(x+z)'s 1 day work=(3/20)+(1/20)

                               =4/20

                               =1/5   [By dividing both denominator and numerator by 4]                                                                                                

=)So,(x+z) can finish the work together in 5 days.

Answer 2

Time taken by X, Y and Z to complete a piece of work= 4 days (given)

Time taken by X and Y to complete the work together= 5 days (given)

Time taken by Y and Z to complete the work together= 10 days (given)

X's one day work= (X+Y+Z)'s 1 day's work - (Y+Z)'s 1 day's work

=> 1/4- 1/10

LCM of 4 and 10= 20

1/4×5/5= 5/20

1/10×2/2=2/20

5/20-2/20= 3/20

X's one day work= 3/20

Z's one day work= (X+Y+Z)'s 1 day's work - (X+Y)'s 1 day's work

=> 1/4-1/5

LCM of 4 and 5= 20

1/4×5/5= 5/20

1/5×4/4= 4/20

5/20-4/20=1/20

Z's one day work= 1/20

Time taken by X and Z to complete the work together= 3/20+1/20

=> 4/20

Reciprocal of 4/20= 20/4

20/4=5

Thus, the time taken by X and Z to complete the work together is 5 days.

HOPE IT WAS HELPFUL.

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