aptitude : : work and wages
 
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Important Formulas
  Exercise
   Exercise 1
1.
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 Rs.760 in 10 days. Find the daily earning of C.
 
A.
Rs.20

B.

Rs.10
C.
Rs.30
D.
Rs.50
   
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Answer: A
Explanation :

Daily earning of A+B+C = (Rs.1350/9) = Rs.150 ……. (1)

Daily earning of A+C = (Rs.470/5) = Rs.94 …….. (2)

Daily earning of B+C = (Rs.760/10) = Rs.76 …… (3)

From (1) and (2); daily earning of B = 150-94 = Rs.56 …..(4)

From (3) and (4); daily earning of C = 76-56 = Rs.20







 
2.
A, B and C together do a piece of work for Rs.53.50. A working alone could do it in 5 days, B working alone could do it in 6 days and C working alone could do it in 7 days. How should the money be divided among them?
 
A.
Rs. 20

B.

Rs.15
C.
Rs.25
D.
Rs.10
   
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Answer: B
Explanation :
A’s share : B’s share : C’s share
= 6*7 : 5*7 : 5*6 = 42 : 35 : 30
A’s share = (53.50/(42+35+30))*42 = (53.50/107)*42 = Rs.21
B’s share = (53.50/107)*30 = Rs.15






 
3.

Two men A and B working together complete a piece of work it work have taken them respectively 12 and 18 days to complete if they worked separately. They received in payment Rs.149.25. Find their shares.

 

 
A.

Rs.59.70     

B.

Rs.60   

C.

Rs.23.45    

D.

Rs.70.10

   
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Answer: A
Explanation :

Wages are distributed in inverse proportion of number of days. Hence,

The money will be divided in the ratio 18 : 12.

A gets (149.25/30)*18 = Rs.89.55 and B gets (149.25/30)*12 = Rs.59.70







 
4.
3 men and 4 boys can earn Rs.756 in days. 11 men and 13 boys can earn Rs.3008 in 8 days. In what time will 7 men with 9 boys earn Rs.2480?
 
A.
(5/3)

B.

(2/5)
C.
(5/6)
D.
(1/2)
   
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Answer: A
Explanation :

(3m+4b) in 1 day earn Rs.(756/7) = Rs.108   ……. (1)

(11m+13b) in 1 day earn Rs.(3008/8) = Rs.376  ….. (2)

From (1), we see that to earn Rs.1 in 1 day, there should be ((3m+4b)/(108)) persons.

Similarly, from (2), to earn Rs 1 in 1 day there should be ((11m+13b)/376) persons.

And also, ((3m+4b)/108) = ((11m+13b)/376)

Or, m(3*376-11*108) = b(108*13-4*376)

=> (m/b) = (100/60) = (5/3)

Now, from (1),

                (3m+4b) in a day earn Rs.108

Or, 3m+4*(3/5)m in 1 days earn Rs.108

Or, (27m/5) in 1 days earn Rs.108

1 m in 1 day earn Rs.((108*5)/27) = Rs.20

Thus, we get that a man earns Rs.20 daily and a boy earns

Rs (20*(3/5)) = Rs.12 daily.

=> 7m+9b earn Rs.(7*20+9*12) = Rs.248 in 1 day.

=> 7m+9b earn Rs.2480 in 10 days.

Note: Since both the LHS and RHS denote the same quantity: “Number. of persons earning Rs.1 in 1 day”.

We can arrive at this step directly be using cross-multiplication-division rule. Arrange the given information as follows:

Men      Boys        Earning    Days

3              4       *          756       ÷    7

11            13     *         3008     ÷     8

Now,

     Men(((3*3008)/8) –((11*756)/7)) = Boys(((13*756)/7)-((4*3008)/8))

Or, m(3*376-11*108) = b(108*13-4*376)

Or,(m/b) = (5/3)







 
5.
Wages for 45 women amount to Rs.15525 in 48 days. How many men must work 16 days to receive Rs.5750, the daily wages of a man being double those of a woman?
 
A.
25 men

B.

27 men
C.
30 men
D.
20 men
   
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Answer: A
Explanation :

Wage of a women for a day = ((15525)/(45*48)) =  Rs.(115/16)

Thus, wage of a man for a day = (2*(115/16)) = Rs.(115/8)

Now, number of men

                =((Total wage)/(No. of days * 1 man’s 1 day’s wage))

                = ((5750*8)/(16*115))

                 = 25 men







 
6.
Two men undertake to do a piece of work for Rs.200. One alone could do it in 6 days, the other in 8 days. With the assistance of a boy they finish it in 3 days. How should the money be didvided?
 
A.
Rs.32

B.

Rs.25
C.
Rs.34
D.
Rs.50
   
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Answer: B
Explanation :

1st man’s 3 days work = (3/6) ; 2nd man’s 3 days work = (3/8)

The boy’s 3 days work = ((1-((3/6)+(3/8))) = (1/8)

Their share will be in the ratio (3/6): (3/8) : (1/8) = 4 : 3 : 1

1st man’s share = (200/8)*4 = Rs.100

2nd man’s share = (200/8)*3 = Rs.75

The boy’s share = (200/8)*1 = Rs.25







 
7.
A, B and C contract a work for Rs.550. Together, A and B are supposed to do (7/11) of the work. How much does C get?
 
A.
Rs.200

B.

Rs.100
C.
Rs.150
D.
Rs.300
   
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Answer: A
Explanation :
A+B did (7/11) work and C did (1-(7/11)) = (4/11) work.
(A+B)’s share : C’s share = (7/11) : (4/11) = 7 : 4
C’s share = (550/11)*4 = Rs.200






 
8.
A,B and C can do a work in 6, 8 and 12 days respectively.Doing that work together they get an amount of Rs.1350. What is the share of B in that amount?
 
A.
Rs.450

B.

Rs.650
C.
Rs.845
D.
Rs.455
   
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Answer: A
Explanation :

A’s one day’s work = (1/6) ; B’s one day’s work = (1/8);

C’s one day’s work = (1/12)

A’s share : B’s share : C’s share = (1/6) : (1/8) : (1/12)

Multiplying each ratio by the LCM of their denominators, the ratios become 4 : 3 : 2

B’s share = ((1350/9)*3) = Rs.450







 
9.
A man can do a work in 10 days. With the help of a boy he can do the same work in 6 days. If they get Rs.50 for that work, what is the share of that boy?
 
A.
Rs.50

B.

Rs.40
C.
Rs.30
D.
Rs.20
   
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Answer: C
Explanation :
The boy can do the work in ((10*6)/(10-6)) = 15 days.
Man’s share : Boy’s share = 15 : 10 = 3 : 2
Man’s share = ((50/5)*3) = Rs.30.






 
10.
A can do a work in 6days and B can do the same work in 5 days.The contract for the work is Rs.220. How much shall B get if both of them work together?
 
A.
Rs.120

B.

Rs.90
C.
Rs.140
D.
Rs.125
   
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Answer: A
Explanation :
A’s 1 day’s work =(1/6) ; B’s work = (1/5)
Ratio of their wages = (1/6) : (1/5) = 5 : 6
B’s share = ((220/(5+6))*6) = Rs.120






 

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