Aptitude - Time and Work - Discussion

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.

The total work for the given no of days will be equivalent to LCM of both the given no of days i.e for 10 days & 2 days LCM will be 10.
So the efficiency of 6M + 8B = 1 unit/day.
now, if we divide it by 2 , then for 3M +4B efficiency will also become 1/2 unit/day.
So for 15M + 20B efficiency will become 5/2 unit /day.
So, total days taken by 15M + 20B for doing the same work = 10 /5/2 =(10*2)/5 = 4days.

Can someone explain it in LCM method?

No need to solve equation:

we have
6x+8y=1/10 ----- (1)
26x+48y=1/2 ------(2)

we want to find: 15x+20y=?----(3)
now taking 2 common form equ(1),
we get:
2(3x+4y)=1/10

So we have, 3x+4y=1/20...ok...
now
in equ 3, take 5 common;
we get:
=5(3x+4y) (3x+4y=1/20)
=5*(1/20)
=4 (ans)

6 men + 8 boys = 10 days -----> (1)
26 men + 48 boys = 2 days -----> (2).

From equation (1) we get,
30 men + 40 boys = 2 days -----> (3)

Given condition,
15 men + 20 boys = ? -----> (4)

Comparing (2) & (3),
4 men = 8 boys, so 1 man = 2 boys.
then for equation (1), 10 men = 10 days.
for equation (4), 25 men = (10x10)25 = 4 days (ans.)

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.

Thanks for explaining this @Zoya.

Hi Sangeetha its very easy to solve this equations.

6x+8y=1/10 ----- (i)
26x+48y=1/2 ------(ii)

Multiply 1st equation into 6, then we get:
36x+48y=1/10*6
26x+48y=1/2

Change the sign of 2nd equation
36x+48y=3/5
-26x-48y=-1/2

The result is
10x=3/5-1/2
10x=1/10
x=1/100

Then apply x value into 1st equation
6x+8y=1/10
6*1/10+8y=1/10
8y=4/100
y=1/200

Thats it.

Here 6 m and 8 b take 10days to complete the work.
It means we can say that, 14 person take 10 days to complete.
So, 1person ---> 1day work is --> 1/140.

We need to find 15 men and 20 boys take how many days. Means 35 person take how many days.
So, 35 person --> 1day work is --> 35/140.
35 person --> 1day work is --> 1/4.

As we know time and work opposite to each other.
so, 35 person take 4 days to complete the work..
Total no of days = 4.

we can also take 2nd equation and our answer is 4.2(approx),
In that case, our equation be like;
74 person takes 2 days to complete,
1 person --> 1 day work is --> 1/148.
so, 35 person --> 1 day work is --> 35/148.
35 person take 4.2.
take approx means our ans is 4 days..

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.