1
Q:

# Relation Between Efficiencies

6 boys and 8 girls finish a job in 6 days and 14 boys and 10 girls finish the same job in 4 days. In how many days working together 1 boy and 1 girl can finish the work?

Q:

M, N and O can complete the work in 18, 36 and 54 days respectively. M started the work and worked for 8 days, then N and O joined him and they all worked together for some days. M left the job one day before completion of work. For how many days they all worked together?

 A) 4 B) 5 C) 3 D) 6

Explanation:

Let M, N and O worked together for x days.

From the given data,
M alone worked for 8 days
M,N,O worked for x days
N, O worked for 1 day

But given that
M alone can complete the work in 18 days
N alone can complete the work in 36 days
O alone can complete the work in 54 days

The total work can be the LCM of 18, 6, 54 = 108 units

M's 1 day work = 108/18 = 6 units
N's 1 day work = 108/36 = 3 units
O's 1 day work = 108/54 = 2 units

Now, the equation is
8 x 6 + 11x + 5 x 1 = 108
48 + 11x + 5 = 108
11x = 103 - 48
11x = 55
x = 5 days.

Hence, all M,N and O together worked for 5 days.

0 26
Q:

P, Q, and R can do a job in 12 days together.  If their efficiency of working be in the ratio 3 : 8 : 5, Find in what time Q can complete the same work alone?

 A) 36 days B) 30 days C) 24 days D) 22 days

Explanation:

Given the ratio of efficiencies of P, Q & R are 3 : 8 : 5

Let the efficiencies of P, Q & R be 3x, 8x and 5x respectively

They can do work for 12 days.

=> Total work = 12 x 16x = 192x

Now, the required time taken by Q to complete the job alone = days.

0 86
Q:

5 men and 3 boys can together cultivate a 23 acre field in 4 days and 3 men and 2 boys together can cultivate a 7 acre field in 2 days. How many boys will be needed together with 7 men, if they cultivate 45 acre of field in 6 days.

 A) 6 B) 4 C) 2 D) 3

Explanation:

Let work done by 1 man in i day be m

and Let work done by 1 boy in 1 day be b

From the given data,

4(5m + 3b) = 23

20m + 12b = 23....(1)

2(3m + 2b) = 7

6m + 4b = 7 ....(2)

By solving (1) & (2), we get

m = 1, b = 1/4

Let the number of required boys = n

6(7 1 + n x 1/4) = 45

=> n = 2.

3 192
Q:

The ratio of efficiencies of P, Q and R is 2 : 3 : 4. While P and R work on alternate days and Q work for all days. Now the work completed in total 10 days and the total amount they get is Rs. 1200. Find the amount of each person(respectively).

 A) 200, 600, 400 B) 400, 600, 200 C) 600, 200, 400 D) 400, 200, 600

Explanation:

Ratio of efficiencies of P, Q and R = 2 : 3 : 4

From the given data,

Number of working days of P, Q, R = 5 : 10 : 5

Hence, ratio of amount of p, Q, R = 2x5 : 3x10 : 4x5 = 10 : 30 : 20

Amounts of P, Q, R = 200, 600 and 400.

0 165
Q:

Two persons Shyam and Rahim can do a job in 32 days together. Rahim can do the same job in 48 days alone. They started working together and after working 8 days Rahim is replaced by a third person Ram whose efficiency is half that of Rahim. Find in how many days the remaining work will be completed by both Shyam and Ram together?

 A) 16 days B) 72/5 days C) 15 days D) 96/5 days

Explanation:

Work done by Shyam and Rahim in 8 days = 8/32 = 1/4

Remaining work to be done by Shyam and Ram = 1 - 1/4 = 3/4

Given efficieny of Ram is half of Rahim i.e, as Rahim can do the work in 48 days, Ram can do the work in 24 days.

One day work of Ram and Shyam = (1/32 - 1/48) + 1/24 = 5/96

Hence, the total work can be done by Shyam and Ram together in 96/5 days.

Therefore, remaining work 3/4 can be done by them in 3/4 x 96/5 = 72/5 = 14.4 days.

2 266
Q:

6 men can complete a piece of work in 12 days. 8 women can complete the same piece of work in 18 days whereas 18 children can complete the piece of work in 10 days. 4 men, 12 women and 20 children work together for 2 days. If only men were to complete the remaining work in 1 day how many men would be required totally?

 A) 38 B) 72 C) 36 D) 76

Explanation:

Given 4men, 12 women and 20 children work for  2 days.

Workdone for 2 days by 4men, 12 women and 20 children =

Therefore, remaining work = 1 - $\frac{1}{2}$ = $\frac{1}{2}$

To complete the same work by only men in 1 day,

We know that M1 x D1 = M2 x D2

Here M1 = 6 , D1 = 12 and M2 = M , D2 = 1

12 x 6 = M x 1

=> M = 12 x 6 = 72

=> But the remaining work = 1/2

Men required => 1/2 x 72 = 36

Only men required to Complete the remaining work in 1 day = 36.

7 566
Q:

Three men, four women and six children can complete a work in 9 days. A women does  double the work a man does and a child does half the work a man does. How many women alone can complete this work in 9 days?

 A) 7 B) 8 C) 9 D) 6

Explanation:

Given (3 Men + 4 Women + 6 Children) -----> 9 days

But W = 2M and C = M/2

Now, convert Men and Children into Women by

Therefore, 7 women alone can complete this work in 9 days.

6 454
Q:

9 girls working 7 hours a day can complete a piece of work in 15 day. In how many days can 6 girls working for 9 hours a day, complete the same piece of work?

 A) 35/4 days B) 17.5 days C) 19 3/4 days D) 37/3 days

Explanation:

Let the number of days be 'p'

As the work is same, we know that

Where M = Men, D = Days, H = Hours per day

Here M1 = 9, D1 = 15, H1 = 7

M2 = 6, D2 = p, H2 = 9

=> 9 x 15 x 7 = 6 x p x 9

=> p = 35/2 = 17.5 days.