Question

Rekha and Meeta can weave a sweater in 12 days meeta and Payal in 15 days payal and Rekha in 20 days in how many days will the weave if the weave together in how many days will each of them weave if they weave it alone .​

Answer 1

Answer:

If Rekha, Meeta and Payal weave together it will take 10 days for them to weave

If Rekha weaves alone it will take 30 days for her to finish the work.

If Meeta weaves alone it will take 20 days for her to finish the work.

If Payal weaves alone it will take 60 days for her to finish the work.

Step-by-step explanation:

• Total work = Number of days of work x Efficiency.

• Let us assume,

Total work = lcm of 12,15 and 20 = 60

If Rekha and Meeta weave in 12 days, their combined efficiency ,$e_{r} +e_{m} = \frac{60}{12} = 5$--------(1)

If Meeta and Payal weave in 15 days, their combined efficiency ,$e_{m} +e_{p} = \frac{60}{15} = 4$--------(2)

If Payal and Rekha weave in 20 days, their combined efficiency ,

$e_{p} +e_{r} = \frac{60}{20} = 3$--------(3)

• Adding equations 1,2 and 3,

$2(e_{r}+ e_{m} +e_{p}) = 12\\e_{r}+ e_{m} +e_{p} = 6$--------(4)

• Solving for individual efficiency,

Subtract 1 from 4,

$e_{p}=1$

Subtract 2 from 4,

$e_{r}=2$

Subtract 3 from 4,

$e_{m}=3$

• Number of days a sweater can be weaved if all of them work together =$\frac{Total work}{e_{r}+ e_{m} +e_{p}} =\frac{60}{6}$ = 10 days

• Number of days a sweater can be weaved if Rekha weaves alone= $\frac{Total work}{e_{r} } = \frac{60}{2}$ = 30 days

• Number of days a sweater can be weaved if Meeta weaves alone=$\frac{Total work}{e_{m} } = \frac{60}{3}$ = 20 days

• Number of days a sweater can be weaved if Payal weaves alone=$\frac{Total work}{e_{p} } = \frac{60}{1}$ = 60 days