# Aptitude Time and Work Test Paper 9

### Work and wages:

41) Two men do a piece of work for rupees 200. One alone can finish the work in 6 days, and the other can finish it in 8 days. With the help of a boy, they finish it in 3 days. How much money should be given to the boy?

1. 30
2. 25
3. 20
4. 15

Explanation:

A can finish the work in 6 days, and B can finish the work in 8 days.
(A+B+C) can finish it in 3 days.

Now, A = 6 days
B = 8 days
A+B+C = 3 days

Note: Assume the total work = LCM of the given days

Take the LCM of days = LCM of (6, 8, and 3) = 24
Let the total work = 24

Or, A's one day work = 24/6=4
B's one day work = 24/8=3
(A+B+C)'s one day work = 24/3=8
Then, C's one day work = 4+3+C = 8, or C=1

Or, A: B: C = 4:3:1
Total money = 200
C's share = [C's one day work/ one day work of (A+B+C)]* total money
C's share = [1/8] * 200 = 25

42) Wages for 45 women amount to rupees 15525 in 48 days. How many men require to work 16 days to receive rupees 5750, the daily wages of a man being double of those of a woman?

1. 25 men
2. 50 men
3. 75 men
4. 20 men

Explanation:

Apply the formula:

M1 * D1 * E1 * W2 = M2 * D2 * E2 * W1

Where E = efficiency or wages, and W = work or amount

ATQ, M1 = 45, D1 = 48, E1 = 1, W1 = 15525
M2 =? D2= 16, E2 = 2, W2 = 5750.

Now, 45 * 48 * 1 * 5750 = M2 * 16 * 2 *15525
Or, M2 = [45 * 48 * 5750]/ [16* 2* 15525]
Or, M2 = 25

Hence, 25 men required.

43) 3 men and 4 children can earn Rs 756 in 7 days. 11 men and 13 children can earn Rs 3008 in 8 days. In what time will 7 men with 9 children earn Rs 2480?

1. 8 days
2. 12 days
3. 15 days
4. None of these

Explanation:

3M + 4C earns 756 in 7 days
Or, (3M +4C)'s one day earning = 756/7 = 108........ (i)

Similarly,

(11M + 13C)'s one day earning = 3008/8 = 376......... (ii)

From equation 1 and 2

3M + 4C = 108
11M + 13C = 376
Multiply equation 1 by 11 and equation 2 by 3 to make the M equal.

11* [3M+4C] = 108 * 11, or, 33M + 44C = 1188....... (iii)

3* [11M+13C] = 376* 3, or, 33M + 39C= 1128....... (iv)

Now subtract equation iv by iii.

i.e., 5C = 60
Or, 1C = 12

That means 1children earns 12 rupees per day
Now, put the children's one day earning, in equation i or ii

3M+ 4C=108
3M + 4 * 12 = 108 or, 3M = 108-48
Or, M = 60/3 = 20

That means 1M earns 20 rupees per day

ATQ, 7M + 9C earns 2480 in D days........ (v)

Now, put the earned value by M and C per day in equation 5.

7*20 + 9*12 = 248
But they earn 2480, i.e., multiply the one day earning by 10, and we get 2480
So, they require 10 days to earn 2480.

44) A, B, and C together earn Rs 1350 in 9 days. A and C together earn Rs 470 in 5 days. B and C together earn 760 in 10 days. Find the daily earning of C.

1. 25
2. 20
3. 12
4. 15

Explanation:

ATQ, (A+B+C) earn 1350 in 9 days
Or, (A+B+C)'s one day earning = 1350/9 = 150....... (i)

Similarly, (A+C)'s one day earning = 470/5= 94...... (ii)

(B+C)'s one day earning = 760/10 = 76........ (iii)

Now, put the value of (B+C) from equation iii, in equation i

A + 76 =150
A's one day earning = 150-76 =74

Now put A's one day earning in eq. ii

A + C = 94
C = 94-74 = 20

Hence, C earns 20 Rs per day.

45) A, B, and C undertakes to do work for Rs 707. A, and B together do 5/7 of the work and rest is done by C alone. How much should C get?

1. 100
2. 300
3. 205
4. 202

Explanation:

Let the work = 7
ATQ, the work done by (A+B) = 5
That means work done by C = 2
Now, (A+B+C) work for 707
So, C's earning = [C's work done/ total work done] * total payment
Hence, C's earning = [2/7]* 707 = 202

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