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 2 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.
Naman Keshari said:
5 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.
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.
(5)
Balaji pawar said:
7 years ago
According to question.
(6m+8B)*10=(26M+48B)*2.
We get ratio man to boy,
M:B=2:1,
Now to calculate total work.
Put this ratio to the above equation,
Let see how,
(6M+8B)*10 = (6*2+8*1)*10=200.
Total work =200.
15 Man And 20 boy can do work in how many day.
Put above ratio to this15 man to20 boy,
(15M+20B)=(15*2+20*1)=50,
Total work =200.
15m+20 b can do work in =200/50,
=4 day.
(6m+8B)*10=(26M+48B)*2.
We get ratio man to boy,
M:B=2:1,
Now to calculate total work.
Put this ratio to the above equation,
Let see how,
(6M+8B)*10 = (6*2+8*1)*10=200.
Total work =200.
15 Man And 20 boy can do work in how many day.
Put above ratio to this15 man to20 boy,
(15M+20B)=(15*2+20*1)=50,
Total work =200.
15m+20 b can do work in =200/50,
=4 day.
Qasim said:
1 decade ago
Hello to all I am confuse in x value.
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.
Then,
x= 1/10/10= 10/1*10= 100/1=100.
Therefore x= 100.
Is it right please any one tell me.
And also tell me why in upward first solution there is x=1/100.
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.
Then,
x= 1/10/10= 10/1*10= 100/1=100.
Therefore x= 100.
Is it right please any one tell me.
And also tell me why in upward first solution there is x=1/100.
Manikanta said:
7 years ago
According to me,
6men + 8boys = 10 days = 60md + 80bd -----> 1 (md = men and days).
26men + 48boys =2 days = 52md + 96bd ----->2
So,
60md + 80bd = 52md + 96bd,
60md - 52md=96bd - 80bd,
8md = 16bd.
1md = 2bd reciprocal of this so we can get 2boys=1men or 1 men = 2boys.
So 15 men and 20 boys in doing the same type of work will be;
40/7.5 = 4.
6men + 8boys = 10 days = 60md + 80bd -----> 1 (md = men and days).
26men + 48boys =2 days = 52md + 96bd ----->2
So,
60md + 80bd = 52md + 96bd,
60md - 52md=96bd - 80bd,
8md = 16bd.
1md = 2bd reciprocal of this so we can get 2boys=1men or 1 men = 2boys.
So 15 men and 20 boys in doing the same type of work will be;
40/7.5 = 4.
Avya bhardwaj said:
5 months ago
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.
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.
(6)
DINESH G said:
9 years ago
06m + 08b = 1/10-------->eq 1.
26m + 48b = 1/2---------->eq 2.
15m + 20b = ?------------->eq 3.
Sol:.
From eq 1 & 2.
60m + 80b = 1.
52m + 96b = 1.
It is equals to 1. So,
60m + 80b = 52m + 96b,
8m = 16b,
M = 2b.
Now substitute in eq 3,
30b + 20b = x.
50b = x---------->eq 4.
Now in eq 1,
12b + 8b = 1/10.
20b = 1/10------->eq 5.
Now compare both eq 4 & 5,
50 * x = 20 * 10.
X = 4 days.
26m + 48b = 1/2---------->eq 2.
15m + 20b = ?------------->eq 3.
Sol:.
From eq 1 & 2.
60m + 80b = 1.
52m + 96b = 1.
It is equals to 1. So,
60m + 80b = 52m + 96b,
8m = 16b,
M = 2b.
Now substitute in eq 3,
30b + 20b = x.
50b = x---------->eq 4.
Now in eq 1,
12b + 8b = 1/10.
20b = 1/10------->eq 5.
Now compare both eq 4 & 5,
50 * x = 20 * 10.
X = 4 days.
Varun bansal said:
1 decade ago
I can suggest a new method:
6 men + 8 boys = 10 days
=> 60 men + 80 boys = 1 day
=> 30 men + 40 boys = 2 days - eq.1.
But given that
26 men + 48 boys = 2 days - eq.2.
From one and two eqns.
4 men = 8 boys.
i.e. 1 man = 2 boys.
From eqn 1. 100 boys = 2 days.
50 boys = 4 days.
30 boys + 20 boys = 4 days.
15 men + 20 boys = 4 days.
6 men + 8 boys = 10 days
=> 60 men + 80 boys = 1 day
=> 30 men + 40 boys = 2 days - eq.1.
But given that
26 men + 48 boys = 2 days - eq.2.
From one and two eqns.
4 men = 8 boys.
i.e. 1 man = 2 boys.
From eqn 1. 100 boys = 2 days.
50 boys = 4 days.
30 boys + 20 boys = 4 days.
15 men + 20 boys = 4 days.
Magic said:
4 weeks ago
First convert it to either boys or men's.
(6m+8b)×10=(26m+48B)×2.
8m = 16B,
m=2B.
One man equals 2 boys.
So, use this in any one of the equation, let's take:
= (6m+8B)×10.
= 6(2B)+8B ×10.
= 200B units.
So, use this trick in and find out the work done boys in the given undefined equation:
= 15m + 20B,
= 15(2B) + 20B,
= 50B.
Calculate total work/ work.
= 200B/50B.
= 4 days.
(6m+8b)×10=(26m+48B)×2.
8m = 16B,
m=2B.
One man equals 2 boys.
So, use this in any one of the equation, let's take:
= (6m+8B)×10.
= 6(2B)+8B ×10.
= 200B units.
So, use this trick in and find out the work done boys in the given undefined equation:
= 15m + 20B,
= 15(2B) + 20B,
= 50B.
Calculate total work/ work.
= 200B/50B.
= 4 days.
(7)
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.
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