Aptitude - Time and Work - Discussion

Given:

6M + 8B = 1/10.
10(6M + 8B) = 1,
60M + 80B = 2,
30M + 40B = 3.
15M + 20B = 4.

To solve this problem, let's assume:

1 man can do 'm' units of work per day
1 boy can do 'b' units of work per day
Total work is 'W' units.

From the given information, we can form two equations:
Equation 1:
(6m + 8b) * 10 = W

Equation 2:
(26m + 48b) * 2 = W

Solving these equations:
From Equation 1:
60m + 80b = W

From Equation 2:
52m + 96b = W

Setting the equations equal to each other:
60m + 80b = 52m + 96b,
8m = 16b,
m = 2b.

Substituting m = 2b in Equation 1:
60(2b) + 80b = W,
120b + 80b = W,
200b = W,
Now, to find the time taken by 15 men and 20 boys:
(15m + 20b) * t = W.

Substituting m = 2b and W = 200b:
(15 * 2b + 20b) * t = 200b,
(30b + 20b) * t = 200b,
50b * t = 200b.
t = 4 days.
Therefore, 15 men and 20 boys will take 4 days to complete the work.

Very Easy to Understand.

6m + 8b = 1/10,
2(3m + 4b) = 1/10,
3m + 4b = 1/20,
5(3m + 4b) = 5(1/20),
15m + 20b = 1/4.

We are getting the solution without the involvement of 26 men and 48 boys.

6 men = 1/10.
1 men = 1/10 * 1/6 = 1/60.

8 boys = 1/10.
1 boy = 1/10 * 1/8 = 1/80.
Now,
15 men = 15/60
20 boys = 20/80

15/60 + 20/80 = 4.
Ans - 4days.

(6M + 8B)× 10 = (26M+48B)×2
30M+40B = 26M+48B
M=2, B=1 {their efficiency}
Now, total work = 6×2+8×10 = 200
therefore work done by 15M + 20B = 200/15×2+20 = 4.

6m + 8b = 1/10.
2(3m + 4b) =1/10.
3m + 4b = 1/20.
5(3m + 4b) = 5(1/20).
15m + 20b = 1/4.

Here in 1st case there are 6 men and 8 boys = [6+8=14] and their work done is 10 so 10*14=140[total workdone by men and boys]
Similarly in 2nd case 26+48=74 , 74*2=140
Total work done by 15 men and 20 boys is 15+20=35 and let their work done be x.
Now 35*x
from the above work done take anyone
140=35*x
x=4

Here in 1st case, there are 6 men and 8 boys = [6+8=14] and their work done is 10.
So, 10*14 = 140[total work done by men and boys,

Similarly,
In 2nd case 26+48 = 74,
74*2 = 140.

The Total work done by 15 men and 20 boys is 15+20=35 and let their work done be x.
Now 35 * x
.
From the above work done take anyone.
140 = 35*x,
x = 4.

6m + 8b = 1/10.
2(3m + 4b) =1/10.
3m + 4b = 1/20.
5(3m + 4b) = 5(1/20).
15m + 20b = 1/4.

From given data,

6M+8B ---> 10days.
26M+48B ---> 2days.
15M+20B ---> t days.

By using Product approach
WF1*T1=WF2*T2.

(6M+8B)*10=(26M+48B)*2,
4M=8B,
M/B=2/1,
M=2;B=1.

Now substitute We get;
20 --->10 days.
100 --->2 days.
50 ---> t days.
100*2=50*t(Product approach)
t=4 i.e.,4 days.