5 boys and 4 girls together can complete a job in 6 hours.

Question

5 boys and 4 girls together can complete a job in 6 hours. If these 5 boys were to complete the work alone taking the same time, they would need to involve 3 men whereas 4 girls with the help of same number of men can complete the work taking just 4 hours. If 4 boys, 4 girls and 1 man together complete the work, how much time will it take?

A. 3 hours
B. 4 hours
C. 5 hours
D. 6 hours
E. 8 hours

A. 3 hours
B. 4 hours
C. 5 hours
D. 6 hours
E. 8 hours

MofeBhatia · Accepted Answer

Firstly, we need to create Hourly rate equation.
Amount of work done by 1 boy(B) in one hour = 1/B, Similarly for 1 Girl(G) = 1/G and 1 Man(M) = 1/M

Now, given that 5 boys + 4 girls can complete the work in 6 hours, so in 1 hour 
5/B + 4/G = 1/6 ---- (1)
Similarly for 5 boys + 3 Men can complete the work in 6 hours, so in 1 hour 
5/B + 3/M = 1/6 ---- (2)
and 4/G + 3/M = 1/4---- (3)

subtracting eq. (2) from (1) , we get 4/ G = 3/M , use this in eq.(3) 
 You will get M = 24 , Substitute M = 24 in eq. (2) , B = 120 and using B, we can get G = 32

Now we need to find 4/G + 4/B + 1/M = 1/W , W = Number of hours taken to complete the work

4/120 + 4/32 + 1/24 = 1/W
W = 5 Hour

chetan2u · Answer

1) 5 boys take same time whether there are 4 girls or three men, so work of 4 girls and 3 men is same.
2) 4 girls and 3 men together, therefore, would mean 4 girls and 4 girls that is 8 girls. So, 8 girls complete a work in 4 hrs. Therefore 4 girls will complete it in 4*2=8 hrs.
3) speed of 3 men is same as that of 4 girls, so 3 men also do it in 8 hrs. Thus 1 man will do it in 8*3=24 hrs.
4) now 5 boys and 4 girls do it in 6 hrs, so (1/5b)+(1/4g)=1/6...
1/(5b)+(1/8)=1/6.....1/(5b)=(1/6)-1/8)=1/24..
So 5 boys do it in 24 hrs, thus 4 boys will do it in 24*5/4= 30 hrs

Thus combined one hour work of 4 girls, 4 boys and 1 man is (1/8)+(1/30)+(1/24)=(15+4+5)/120=24/120=1/5...
So if (1/5)the work is done in one hour, then the entire work will be done in 5 hours..

C

akurathi12 · Answer

5 boys and 4 girls together can complete a job in 6 hours. If these 5 boys were to complete the work alone taking the same time, they would need to involve 3 men whereas 4 girls with the help of same number of men can complete the work taking just 4 hours. If 4 boys, 4 girls and 1 man together complete the work, how much time will it take?

A. 3 hours
B. 4 hours
C. 5 hours
D. 6 hours
E. 8 hours

A. 3 hours
B. 4 hours
C. 5 hours
D. 6 hours
E. 8 hours

ksrutisagar · Answer

Let b, g, and m be the respective rates of each boy girl and man

5b + 4g = (1/6) ..... Eqn 1 ( Since time = 6 hours)

5b + 3m = (1/6) ......Eqn 2 ( Since time = 6 hours)

4g + 3m = (1/4) ......Eqn 3 ( Since time = 4 hours )

4b + 4g + 1m = ? ... Reqd Case

5b + 4g = 5b + 3m From Eqn 1 and Eqn 2

4g = 3m

1.5 (5b + 4g )= 4g + 3m From Eqn 1 and Eqn 3

7.5b = 1.5m or 5b = m

In The required case compared to the case in equation 1, 1 boy has been replaced by 1 man ( who is faster than the boy)

So time ( t ) will be less than 6 hrs

Similarly comparing The required case with the case in Eqn 3

In Eqn 3 , 4 girls and 3 men take 4 hours

While in the required Case , there are 4 boys, 4 girls and 1 man

i.e 2 men have been replaced by 4 boys

Since 5b = m, Time ( t ) will be more than 4 hours ( Time taken in Eqn 3 )

So, 4 < t < 6

Only t = 5 satisfies

Choice C

Bunuel · Answer

______________________
Merging topics.

exc4libur · Answer

r=d/t

5b+4g=1/6, 5b+3m=1/6, 4g+3m=1/4
4g-5b= =1/12
8g=1/6+1/12=3/12=1/4, g=1/32
5b+4(1/32)=1/6, b=1/120
5b+3m=1/6, 5/120+3m=1/6, m=1/24

4b+4g+m=1/t
4/120+4/32+1/24=1/t
1/30+1/8+1/24=1/t
lcm(5*2*3;2^3;3*2^3)=5*8*3=120
 /120=1/t
t=120/24=5

Ans (C)

KarishmaB · Answer

Establish equivalence first. (5B + 4G) take 6 hours. Since (5B + 3M) also take 6 hours, 3M = 4G (3M + 4G) take 4 hours and 3M = 4G, so this means 3M take 8 hours alone and 4G take 8 hours alone. Then Rate of work of 1 man = 1/24 Rate of work of 4 girls = 1/8 ext{Rate of 5 Boys} = \frac{1}{6} - \frac{1}{8} = \frac{1}{24} ext{Rate of 4 boys} = \frac{4}{24*5} = \frac{1}{30} ext{Combined rate of 1 M + 4B + 4G} = \frac{1}{24} + \frac{1}{8} + \frac{1}{30} = \frac{1}{5} Time taken = 5 hours. Answer (C) Work rate discussed here: https://youtu.be/88NFTttkJmA

5 boys and 4 girls together can complete a job in 6 hours.

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5 boys and 4 girls together can complete a job in 6 hours.

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