5 men and 4 boys can do a piece of work in 15 days while 4 men and 3 boys can do the same work in 15 days. In how many days can 2 men and 1 boy do the work?

Options
- 12 days
- 14 days
- 18 days
- None

CORRECT ANSWER : None

Discussion Board
answer

From the problem statement, we have:

First equation:
5 men and 4 boys complete the work in 15 days

15
(
5
??
+
4
??
)
=
1
(Total work is 1 unit)
15(5M+4B)=1(Total work is 1 unit)
5
??
+
4
??
=
1
15
(Work done in one day)
5M+4B=
15
1
?
(Work done in one day)
Second equation:
4 men and 3 boys complete the work in 15 days

15
(
4
??
+
3
??
)
=
1
15(4M+3B)=1
4
??
+
3
??
=
1
15
(Work done in one day)
4M+3B=
15
1
?
(Work done in one day)
Step 2: Solving for M and B
We solve the system of equations:

5
??
+
4
??
=
1
15
5M+4B=
15
1
?

4
??
+
3
??
=
1
15
4M+3B=
15
1
?

Multiply the second equation by 5 and the first equation by 4:

20
??
+
15
??
=
4
15
20M+15B=
15
4
?

20
??
+
16
??
=
4
15
20M+16B=
15
4
?

Subtracting the second equation from the first:

(
20
??
+
15
??
)
-
(
20
??
+
16
??
)
=
4
15
-
4
15
(20M+15B)-(20M+16B)=
15
4
?
-
15
4
?

-
??
=
0
?
??
=
0
-B=0?B=0
Substituting
??
=
0
B=0 into
4
??
+
3
??
=
1
15
4M+3B=
15
1
?
:

4
??
=
1
15
4M=
15
1
?

??
=
1
60
M=
60
1
?

Step 3: Finding Time for 2 Men and 1 Boy
The work done per day by 2 men and 1 boy:

2
??
+
1
??
=
2
×
1
60
+
0
=
2
60
=
1
30
2M+1B=2×
60
1
?
+0=
60
2
?
=
30
1
?

Thus, the number of days required to complete the work:

1
1
30
=
30
 days
30
1
?

1
?
=30 days
Final Answer:30 days

pand 03-5-2025 12:18 PM

Maths

5m+4b=1/15....1
4m+3b=1/15....2

Multiply equation 1by4 and 2by5....and then subtract 3&4 that equations......we get
20m+16b=4/5......3
20m+15b=1/3.......4
- - -
b=-1/15
Now,equating the value of b in eq4, we get
20m+15(-1/15)=1/3
m=1/15

Now,2m+b=
2(1/15)-1/15=1/15
=15 days
Ans:None



Smit shah 03-20-2021 07:15 AM

Wrong question

5M+4B = 15d, then if we decrease both men and boys, then days also has to be increased but here it''s same. How?

4M+3B=15d

Rajarajan 12-19-2020 01:09 AM

Electrician

Nice

Manish 03-3-2019 07:48 AM

solution

5m + 4b = 1/15 ---a
4m + 3b = 1/15 ---b
(4*b)-(3*a)
5m=1/15
m=1/75
a---- 4b=0
b=0
2m + 1b = 2*1/75 = 37.5 days

b2 09-20-2018 07:55 AM

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