Aptitude - Time and Work - Discussion

Here 6 men and 8 boys take 10 days to complete the work.
In the same way, 26 men and 48 boys take 2 days to do the same work.
Clearly, by common we can say 1men=2 boys.
So we can covert the no.of men into boys
And by take their one day work and cross multiplying it, we will get the answer.
Therefore =6men*2+8boys=1/10.
And 15men*2+20boys=?.
20=1/10,
50=?,
Therefore, ?=1/4 (one day work).
Total mo of day=4.

Can't understand this 2 equation. Please, anyone, explain.

If X is the overall work then,
X=10(6m+8b)=60m+80b-----1st eqn.
X=2(26m+48b)=52m+96b-----2nd eqn.

Equating the both eqns 1 and 2
We get m:b=1:2 it means 1man equal to 2 boys so 15m+20b=30b+20b=50b.

From eqn 1,12b+8b=20b can do in 10days.
Then cm to 20b=10.
50b=y.
Y=4 days.

If 6 men and 8 boys take 10days to complete a work.
Which means 3 men and 4 boys take 20days to complete a work.
Then 3*5 (15 men) and 4*5(20 boys) take (20/5) which is 4 days.

(6M+8B)10=(26M+48B)2.

8M=16B.
M:B
2:1.

12B + 8B-----10days
30B + 20B------?

=> 20/50 *10=4days.

Given that.

6M+8B = 1/10 (1'd work). ----------------[1].

26M+49B = 1/2 (1'd work). ----------------[2].

Sub eq (2) - eq (1).

20M+40B = 1/2-1/10=4/10.

2M+4B = 4/100 = 1/25.

Total time 25.

Manpower 6M+8B 26M+48B
Rate 1 5
Time 10 2
Work 10 10

From this use M1*R1*T1/W = M2*R2*T2/W2.
We will get 30M+40B = 26M+48B.

From this equation, we can see that if 4 men are decreased then 8 boys are required to do the same work at the same time.

Now, we need to find the days required for 15M+20B.
15M+20B is nothing but 25 men. (because of 1 man = 2 boys).

Now if we find the rate at which 15M+20B works T can be easily calculated.

To find the rate,
Take 6M+8B works at rate of 1. i.e 10 men work at rate of 1.
We need to find rate at which 25 men will work.
therefore,10 men at rate of 1,20 men at 2 and hence 25 at 2.5.

Manpower 6M+8B 26M+48B 15M+20B
Rate 1 5 2.5
Time 10 2 4
Work 10 10 4

you can do this mentally pretty fast if practiced.

Apply the value of x = 1/100 in Eqn 1, we get,
6/100+8y = 1/10.

Take LCM you will get the answer y = 1/200.

Good, thanks @Ritik.

6x+8y = 1/10,
2(3x+4y) = 1/10,
3x+4y = 1/20,

Both side multiple with 5,
15x+20y = 1/4.

So 1/4 work completes = 1 day.
total work = 4days.