# 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 1 of 20.

Harun Sobbosachi said:   7 years ago
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.)
(3)

Anshul said:   5 years ago
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.

Bhushan said:   4 years ago
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..
(3)

Javid Mir said:   9 years ago
Hello all, I will show you how to obtain X & Y in above question:

Here we have two equations:

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

Divide (i) by (ii) we get,

6x+8y/26x+48Y = 1/10 X 2/1 (Divide sing on changing to multiply sing inverses the quantities).

Two 2 common.

2(3x+4y)/2(13x+24y) = 1/5 (cancel 2 in both nominator & denominator).

3x+4y/13x+24y = 1/5.

On cross multiplication we get,

15x+20y=13x+24y on rearranging x & y variable on either sides we get,

15x-13x = 24y-20y.
2x = 4y.

x = 4y/2 => x = 2y,

Now substitute the value of x in equation.........(i).

6x+8y = 1/10 =>
6X2y+8y = 1/10.

12y+8y = 1/10 =>
20y = 10 or y = 1/200.

Hence x = 2y i.e. x = 2 x 1/200.

i.e x = 1/100.

Rorororo said:   6 years ago
Let M denotes the work done by a man in 1 day and B denotes the work done by a boy in 1 day.

Now, 6 men and 8 boys do the work in 10 days means 10(6M+8B) = 1.

Similarly, 26 men and 48 boys do the work in 2 days means 2(26M+48B) = 1.
=> 10(6M+8B) = 2(26M+48B),
=> 60M + 80B = 52M + 96B,
=> 8M = 16B,
=> 1M = 2B.

Thus, if we employ 15 men and 20 boys, we mean to say; 15M + 20B.
= 30B + 20B = 50B.

Now, (6M + 8B) do the work in 10 days.
=> (12B + 8B) do the work in 10 days.
=> 20B do the work in 10 days.
=> 1B do the work in 10*20 = 200 days.
=> 50B will do the work in 200/50 = 4 days.
(1)

Harish Raj said:   1 decade ago
Here is my approach.

Add the men and boys in each seniario which will be like the following,

6+8= 10 so (14 persons can do the work in 10 days) -- 1
26+48=74 so, (76 persons can do the work in 2 days) --2

now the question is, 20+15 i.e (35 person can do the work in how many days?)

take the second senario,

if 74 person can do the work in 2 days, 35 person do it in approx 4 (less than) days.

There is no Answer given less than 4, s0 we can take 4 as answer. simple. (CAT needs smart work than hard work)

Nitesh.s.naik said:   4 years ago
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.

Pravas said:   8 years ago
We can do also,
(6m + 8b) * 10 = (26m + 48B) * 2,
=> 60m + 80b = 52m + 96b,
=> 8m = 16b,
=> m/b = 16/8 = 2 : 1.

Total work = (6m + 8b) * 10.
= (6 * 2 + 8 * 1) * 10 = 200.

As per question, 15 men and 20 boys will do the same work in => (15 * 2 + 20 * 1) = 50 i.e That is m/b = 2 : 1.
Total days = total work/total men and boys => 200/50 = 4 days.
(2)

Jabi Mir said:   10 years ago
We have two equations; 6x + 8y = 1/10 & 26x + 48y = 1/2.

We can write them as' 60x + 80y = 1 ...(1) & 52x + 96y = 1 ...(2).

Since work is same, equation 1 = equation 2.

i.e, 60x+ 80y = 52x+ 96y => 60x-52x = 96y-80y => 8x = 16Y.

or x/y = 16/8 => x=2y, Now substitution value of x in = n(1).
60 x 2y + 80y =1 => 120y +80y = 1.
or, 200y = 1 or y = 1/200.

Similarly, Now we can calculate value of x by substituting value of Y in any equation above.

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)