Question

Qus1. 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 they weave it, if they weave together ? In how many days will each of them weave, if they weave it alone?

Answer 1

let
regha =a

meetha =b

payal = c

meera = d

Rekha and Meeta can weave a sweater in 12 days

ie a &b = 12 days

a+b = 12 --------------------------equation (1)

Meeta and Payal in 15 days

ie b&c = 15

b+c = 15------------------------------------(2)
Payal and Rekha in 20 days.

ie a &c = 20 days

a+c = 20 -----------------------------------(3)


combining (1) and (2)
(2)-(1)

a+b = 12
b+c = 15
-----------------
3= c-a ------(4)

now combining (2) and (3) [(3)-(2)]

b+c = 15
a+c = 20
----------------
5= a-b ---------------(5)

comparing the (5) and (1)
(5)+(1)

5= a-b
12=a+b
--------------
17= 2a

a=17/2

apply this in (1)

a+b =12

17/2+b =10
b= 10-7/2
= 13/2 days

now apply this in (2)


b+c = 15

13/2+c =15
c= 15-13/2
= 17/2

if the work all together

= a+b+c = 17/2+13/2+17/2 = 47/2 days
if
they weave it alone

days taken by a =17/2 days

days taken by b= 13/2 days

days taken byc = 17/2 days