# Aptitude - Time and Work - Discussion

Discussion Forum : Time and Work - General Questions (Q.No. 6)
6.
If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:
4 days
5 days
6 days
7 days
Explanation:

Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.

 Then, 6x + 8y = 1 and 26x + 48y = 1 . 10 2

 Solving these two equations, we get : x = 1 and y = 1 . 100 200

 (15 men + 20 boy)'s 1 day's work = 15 + 20 = 1 . 100 200 4

15 men and 20 boys can do the work in 4 days.

Discussion:
193 comments Page 2 of 20.

Sajid said:   2 years ago
6M+8B *10 = 26M + 48B*2.
4M = 8B.

Ratio M&B = 2/1.
Total work = 2(6M+8B) * 10.
200.

Acc to question.
15M+20B=? ,
2(15M+20B),
50.

TIME = 200/50 = 4 Days.
(12)

Devil said:   2 years ago
Thanks for the good explanation @Parkavi.
(1)

Waseem said:   2 years ago
Thanks for explaining this @Zoya.
(4)

Nav Raj Bhatta said:   3 years ago
Find the relation between first, second to third equation.

6M+8B=10
26M+48B=2
15M+20B=?.

Now taking first equation;
6M + 8B = 10.
60M + 80B = 1.
30M + 40B = 2.
15M + 20B = 4.
(63)

Kriti said:   3 years ago
6men, 8boys take 10 days.
(6men, 8boys)*5 i.e. 30men ad 40boys take 2 days to complete the work.
Let 15men, 20boys take x days.
(15men, 20boys) * 2 take (x/2)days.
hence 2 = (x/2),
x = 4.
(3)

Parkavi said:   3 years ago
(6m+8b)*10 = (26m + 48b) * 2.
(6m+8b)*5= (26m + 48b),
20m+40b =26m + 48b.
4m. = 8b,
M/b = 2/1.

Now;
(6*2+8*1) * 10 = (15 * 2 + 20 * 1) * X.
12+8 ) * 10 = (30+20) * X,
200. = 50 * X.
X = 4.
(30)

Raza said:   3 years ago
6x+8y = 1/10----------(1)

Taking 2 common on LHS
3x+4y = 1/20,
Multiply it by 5 on both side,
15x+20y = 4.
(12)

Jigme Wangchuk said:   4 years ago
Can someone explain it in LCM method?
(6)

Given :

6M + 8B = 10
26M + 48B = 2
To find 15M + 20M =?

=> Remember :- Worker increases Days decreases.

6*2+3 is 15.
8*2+4 is 20.
4-3= 1,
So 10Ã·2-1 = 4 days.
(1)

Naman Keshari said:   4 years ago
Hi everyone!.

In this question, the simplest way to solve it is:

6 men and 8 boys take 10 days.

Therefore, 6:8 = 10 which implies 3:4 = 10 (2 being the common factor in the ratio).
Similarly, 26:48 = 2 which implies 13:24 = 2 (2 being the common factor in the ratio).
We have to find 15:20 = how many days? right?

Now 15:20 = 3:4 (5 being the common factor here).
Now since 6:8 and 15:20 has the same ratio;
Therefore, (2/5) x 10 = 4 days.
(4)