Question

A work is being completed by a group of 10 men in 12 days. Same work
is completed by a group of 10 women in 6 days. In how many days will
the work be completed if both the groups work together?
(a) 4
(b) 6
(c) 9
(d) 18​

Answer 1

Gɪᴠᴇɴ :-

• 10 Men complete a work in = 12 Days.
• 10 women complete same work in = 6 Days.

Tᴏ Fɪɴᴅ :-

• In how many days will the work be completed if both the groups work together?

Sᴏʟᴜᴛɪᴏɴ :-

Since work is same in Both case we can say That,

→ 10M * 12 = 10W * 6

→ 2M = 1W

So,

→ 2M = 1W

→ 10M = 5W .

Therefore,

→ Whole Group = 10M + 10W = 5W + 10W = 15W.

Now,

→ 10 women can complete work in = 6 Days.

→ 1 women will complete same work in = (6 * 10) Days.

→ 15 women will complete same work in = (6*10)/15 = 4 Days. (Ans.)

Hence, Both the groups working together complete the same work in 4 Days.

Answer 2

Given :

• 10 men's one day's work = 12 days

• 10 women's one day's work = 6 day's

To find :

• The work be completed if both the groups work together = ?

Step-by-step explanation :

According to the question :

10 men's one day's work = 1/12

∴ 1 man one day's work = 1/12

= 1/12 × 10

           = 1/120

Similarly,

1 woman one day's work = 1/6 × 10

           = 1/60

∴ ( 1 man + 1 woman) 's one days,

            = 1/120 + 1/60

            = 1 + 2/120

            = 3/120

            = 1/40

∴ ( 10 man + 10 woman) 's are day's work

= 10/40

              = 1/4

Therefore, both the team can finish the whole work in 4 days .

Hence,

Option (a). 4 days is the correct option ✔️