Question

Example 2.11
X. Y and Z can do a piece of job in 4, 6 and 10 days respectively.
If X.Y and Z work together to complete, then find their separate
shares if they will be paid 3100 for completing the job.​

Answer 1

Answer:

x=2810 y=7777 this is answer

Answer 2

If they will be paid 3100 for completing the job, then the share of X is Rs. 1500, Y is Rs. 1000 and Z is Rs. 600.

Step-by-step explanation:

X alone can do a piece of work in 4 days  

So, work done by X in 1 day = $\frac{1}{4}$

Y alone can do a piece of work in 6 days  

So, work done by Y in 1 day = $\frac{1}{6}$

Z alone can do a piece of work in 10 days

So, work done by Z in 1 day = $\frac{1}{10}$  

It is also given that if X, Y and Z together complete a job then they will be paid Rs. 3100.  

We know that the wages are shared on the basis of work done and the work done is reciprocal of the time taken to do that work, therefore,

The ratio of work done by X, Y & Z is,

= $\frac{1}{4}$ : $\frac{1}{6}$ : $\frac{1}{10}$

Multiplying by the L.C.M of 4, 6 & 10 = 60 throughout  

= 15 : 10 : 6

Thus,

(i)The share of X from the total money will be,

= $\frac{15}{15+10+6}$ × 3100

= $\frac{15}{31}$ × 3100

= Rs. 1500

(ii) The share of Y from the total money will be,

= $\frac{10}{15+10+6}$ × 3100

= $\frac{10}{31}$ × 3100

= Rs. 1000

(iii) The share of Z from the total money will be,

= $\frac{6}{15+10+6}$ × 3100

= $\frac{6}{31}$ × 3100

= Rs. 600

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