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:
Answer: Option
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:
202 comments Page 15 of 21.
Jabi Mir said:
1 decade 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.
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.
Atul1487 said:
1 decade ago
We can do this in single step.
6 men and 8 boys can do work in 10 days.
So 6m+8b=1/10.
So we have to find 15m+20b=?
6m+8b=1/10.
Divide each term by 2 in both side we get,
3m+4b=1/20.
And multiply each term with 5.
15m+20b=5*120.
15m+20b=1/4.
So answer is 4 days simple.
6 men and 8 boys can do work in 10 days.
So 6m+8b=1/10.
So we have to find 15m+20b=?
6m+8b=1/10.
Divide each term by 2 in both side we get,
3m+4b=1/20.
And multiply each term with 5.
15m+20b=5*120.
15m+20b=1/4.
So answer is 4 days simple.
Ramya said:
1 decade ago
If they give 'or' instead of 'and' means we have to take + only.
Ex: 6 men and 8 boys.
6 men or 8 boys.
Ex: 6 men and 8 boys.
6 men or 8 boys.
BLM said:
1 decade ago
We can solves these types of question by using simple formula: M1*D1 = M2*D2.
6M+8B =10D......1.
26M+48B =2D.....2.
15M+20B +?......3.
M1DI + M2D2.
From eq 1 and 2.
(6M+8B)*10 = (26M+48B)*2.
By solving we get,
1M=2B.
Now from eq 1 and 3, use the same formula. Substitute the value of man of boy.
(6M+8B)*10 = (15M+20B)*D2.
(6M+4M)*10 = (15M+10M)*D2.
D2 = 4 days.
6M+8B =10D......1.
26M+48B =2D.....2.
15M+20B +?......3.
M1DI + M2D2.
From eq 1 and 2.
(6M+8B)*10 = (26M+48B)*2.
By solving we get,
1M=2B.
Now from eq 1 and 3, use the same formula. Substitute the value of man of boy.
(6M+8B)*10 = (15M+20B)*D2.
(6M+4M)*10 = (15M+10M)*D2.
D2 = 4 days.
Akash kumar said:
1 decade ago
A and B can do a work in 12 and B and C in 16 days.
If A does work for 5 days and B for 7 days and then remaining work is completed by C in 13 days then C can Do this work in how many days?
If A does work for 5 days and B for 7 days and then remaining work is completed by C in 13 days then C can Do this work in how many days?
Vikram sihag said:
1 decade ago
6m+8b = 10 days.
60m+80b =1 day eq.1.
15m+20b = ? eq.2.
Because eq.1 is 4 times eq.2, So ans is 4 days.
60m+80b =1 day eq.1.
15m+20b = ? eq.2.
Because eq.1 is 4 times eq.2, So ans is 4 days.
PRAVEEN K PILLAI said:
1 decade ago
6 men X 10= 60
8 men X10 = 80 i.e 60m = 80b.
So 1 men = 4/3 boys, So 6 men = 6 x 4/3-8 boys.
So 8+8 = 16 boys completes work in 10 days.
Now the case of 15 men and 20 boys.
15 men = 15 x 4/3 = 20 boys, So 15 men and 20 boys = 40 boys.
If 16 boys can do a work in 10 days then 40 boys will be able to do in 16 x10/4 = 4 days.
8 men X10 = 80 i.e 60m = 80b.
So 1 men = 4/3 boys, So 6 men = 6 x 4/3-8 boys.
So 8+8 = 16 boys completes work in 10 days.
Now the case of 15 men and 20 boys.
15 men = 15 x 4/3 = 20 boys, So 15 men and 20 boys = 40 boys.
If 16 boys can do a work in 10 days then 40 boys will be able to do in 16 x10/4 = 4 days.
Zoya said:
1 decade ago
M1*D1/W1 = M2*D2/W2.
14[men + boys]*10 /1 = 35 * D2 /1.
14*10/35 = D2.
D2 = 4.
14[men + boys]*10 /1 = 35 * D2 /1.
14*10/35 = D2.
D2 = 4.
V nirmal kumar said:
1 decade ago
6 men and 8 boys are in the ratio 6:8=3:4.
15 men and 20 boys are also in the same ratio 15:20=3:4.
Common factor for the first combination is 2 and common factor for the second combination is 5.
So if it take 10 days for the first combination then.
5 : 2.
10 : ?
= 4.
As you can see the common factors are in the ratio of the number of days needed to finish the work.
15 men and 20 boys are also in the same ratio 15:20=3:4.
Common factor for the first combination is 2 and common factor for the second combination is 5.
So if it take 10 days for the first combination then.
5 : 2.
10 : ?
= 4.
As you can see the common factors are in the ratio of the number of days needed to finish the work.
Pradeep Oram said:
1 decade ago
@Sidharth.
There is also mentioned 2nd eq. i.e 26x+48y = 1/2.
And it doesn't relate to 3rd eq.
It may your procedure is quite wrong?
There is also mentioned 2nd eq. i.e 26x+48y = 1/2.
And it doesn't relate to 3rd eq.
It may your procedure is quite wrong?
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