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:
198 comments Page 3 of 20.
Meera said:
1 decade ago
Hi Sangeetha its very easy to solve this equations.
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
x=1/100
Then apply x value into 1st equation
6x+8y=1/10
6*1/10+8y=1/10
8y=4/100
y=1/200
Thats it.
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
x=1/100
Then apply x value into 1st equation
6x+8y=1/10
6*1/10+8y=1/10
8y=4/100
y=1/200
Thats it.
(3)
Bikash Choudhury said:
10 years ago
It is simple method.
6m-----+8w-------- = 10.
6*10=60----8*10---- = 80....equation 1.
26m------+48w-------- = 2.
26*2=52------48*2=96....equation 2.
Equation 1- Equation 2.
60-52 = 8 and 96-80 = 16.
8:16 = 1:2.
12w+8w = 10.
=> 20w = 10.
=> 1w = 20*10.
We have to find 15m+20w = ?
=> 30w+20w = 50w = 200.
=> w = 200/50 = 4 days.
6m-----+8w-------- = 10.
6*10=60----8*10---- = 80....equation 1.
26m------+48w-------- = 2.
26*2=52------48*2=96....equation 2.
Equation 1- Equation 2.
60-52 = 8 and 96-80 = 16.
8:16 = 1:2.
12w+8w = 10.
=> 20w = 10.
=> 1w = 20*10.
We have to find 15m+20w = ?
=> 30w+20w = 50w = 200.
=> w = 200/50 = 4 days.
Krishna said:
1 decade ago
(6M & 8B)10Days > (60M & 80B)..(1).
(26M & 48B)2Days > (52M & 96B)...(2).
Subtract 1 And 2 We get 8M & 16B.
Time Taken To Complete the work = Ratio= 2(M):1(B).
Now, (15M & 20B) = ? ...(03).
Put the ratio of 2:1 in (03),
We get 50.
Also put ratio in (1),
we get 200.
So total work/M + B = 200/50 = 4days.
(26M & 48B)2Days > (52M & 96B)...(2).
Subtract 1 And 2 We get 8M & 16B.
Time Taken To Complete the work = Ratio= 2(M):1(B).
Now, (15M & 20B) = ? ...(03).
Put the ratio of 2:1 in (03),
We get 50.
Also put ratio in (1),
we get 200.
So total work/M + B = 200/50 = 4days.
YASEEN said:
2 years ago
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.
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.
(69)
Srujan said:
9 years ago
If you practice well this would be a short cut.
(6Men + 8Boy).10 = (26Men + 48Boy).2.
=> (6Men + 8Boy).5 = (26Men + 48Boy).1.
30m => 48B
26m =>40B
------------------
4m = 8B
1Men = 2Boy
15Men + 20Boy = 25Men
6men + 4men = (1men = 2Boy)
10men --> 10days
25men---?
So,
10*10 = 25*D
D = 4days.
25men = 15men + 20boy = 4days.
(6Men + 8Boy).10 = (26Men + 48Boy).2.
=> (6Men + 8Boy).5 = (26Men + 48Boy).1.
30m => 48B
26m =>40B
------------------
4m = 8B
1Men = 2Boy
15Men + 20Boy = 25Men
6men + 4men = (1men = 2Boy)
10men --> 10days
25men---?
So,
10*10 = 25*D
D = 4days.
25men = 15men + 20boy = 4days.
Arun said:
2 years ago
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.
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.
(40)
Purushottam Kumar said:
9 years ago
(6m+8b)*10 = (26m+48b)*2.
=> (6m+8b)*5 = 26m+48b.
=> 30m+40b = 26m+48b.
=> 4m = 8b.
=> m = 2b.
=> m/b = 2x/x (let).
Now, total work = (6m+8b)*10.
=> (6*2x+8*x)*10.
=> 200x.
Now, (15m+20b)*n = 200X (where n is required number of days).
=> (15*2x+20*x)*n = 200x.
=> (50x)*n = 200x.
=> n = 4 days.
=> (6m+8b)*5 = 26m+48b.
=> 30m+40b = 26m+48b.
=> 4m = 8b.
=> m = 2b.
=> m/b = 2x/x (let).
Now, total work = (6m+8b)*10.
=> (6*2x+8*x)*10.
=> 200x.
Now, (15m+20b)*n = 200X (where n is required number of days).
=> (15*2x+20*x)*n = 200x.
=> (50x)*n = 200x.
=> n = 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.
Sai naresh said:
7 years ago
Hi, I am Sai Naresh.
Another simple way of solving the 6th question.
(M*D*H)/W=(M*D*H)/W.
By using this formula we can do many ques.
(M) Men, it may be boy or girl just add up.
D days.
H hours.
W work.
If, data is not mentioned just remove what u don't need.
14*10=74*2=35*X.
BY EQUATING 14*10=35*X.
X = 140/35 = 4days.
Another simple way of solving the 6th question.
(M*D*H)/W=(M*D*H)/W.
By using this formula we can do many ques.
(M) Men, it may be boy or girl just add up.
D days.
H hours.
W work.
If, data is not mentioned just remove what u don't need.
14*10=74*2=35*X.
BY EQUATING 14*10=35*X.
X = 140/35 = 4days.
Vijay said:
8 years ago
Guys. No need to get in to the equation. If 6 man and 8 boys can do a work in 10 days. So obviously 12 men's and 16 boys can complete this in 5 days. (Since the count of the mens and boys is 15 and 20 respectively. So the number of the day will be reduce more. So the only option is 4 which is below 5) so the answer is 4.
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