1). A can do a piece of work in 9 days and B can do the same work in 15 days. If they work together, in what ratio A and B will receive their wages?
A). 3 : 5 
B). 5 : 3 
C). 2 : 5 
D). 5 : 2 
Correct Answer: 5 : 3
A's 1 day's work = \( \Large \frac{1}{9} \)
B's 1 day's work = \( \Large \frac{1}{15} \)
A's share : B's share = \( \Large \frac{1}{9} \) : \( \Large \frac{1}{15} \)
= \( \Large \frac{5}{45} \) \( \Large \frac{3}{45} \) = 5 : 3 
2). A can do a piece of work in 3 days while B can do the same work in 4 days. If they work together for a total wages of Rs.2800, how much does A get?
A). Rs.1200 
B). Rs.1900 
C). Rs.1300 
D). Rs.1600 
Correct Answer: Rs.1600 A's 1 day's work = \( \Large \frac{1}{3} \)
B's 1 day's work = \( \Large \frac{1}{4} \)
A's share : B's share = \( \Large \frac{1}{3} \) : \( \Large \frac{1}{4} \)
= \( \Large \frac{4}{12} \) \( \Large \frac{3}{12} \) = 4 : 3
A's share = \( \Large \frac{4}{7} \times 2800 \)
= \( \Large 4 \times 400 \) = Rs.16000

3). A alone can do a piece of work in 3 days, while B alone can do the same work in 2 days. If they work together to complete the work, their total wages is fixed Rs.225. Find the share of A.
A). Rs.90 
B). R.s.75 
C). Rs.95 
D). Rs.65 
Correct Answer: Rs.90
A's 1 day's work = \( \Large \frac{1}{3} \)
B's 1 day's work = \( \Large \frac{1}{2} \)
A's share : B's share = \( \Large \frac{1}{3} \) : \( \Large \frac{1}{2} \)
= \( \Large \frac{2}{6} \) : \( \Large \frac{3}{6} \) = 2 : 3
Share of A = \( \Large \frac{2}{5} \times 225 \) = Rs.90 
4). A can finish a work in 15 days, B in 20 days and C in 25 days. All these three worked together and earned Rs.4700. The share ofC is
A). Rs.1200 
B). Rs.1500 
C). Rs.1800 
D). Rs.2000 
Correct Answer: Rs.1200 A's 1 day's work = \( \Large \frac{1}{15} \)
B's 1 day's work = \( \Large \frac{1}{20} \)
C's 1 day's work = \( \Large \frac{1}{25} \)
A, B and C worked together.
Therefore, \( \Large \left(A+B+C\right) \)'s 1 day's work
= \( \Large \frac{1}{15} \)+\( \Large \frac{1}{20} \)+\( \Large \frac{1}{25} \)
= \( \Large \frac{20+15+12}{300} = \frac{47}{300} \)
Days taken to complete work by A, B and C working together
= \( \Large \frac{300}{47}\)
Therefore, Share of C = \( \Large \frac{1}{25} \times \frac{300}{47} \times 4700 \) = Rs.1200

5). A person can do a piece of work in 26 days and an another person can do the same work in 39 days. If they work together, then by what per cent the wages of 1st person is more than that of 2nd person?
A). 25% 
B). 35% 
C). 15% 
D). 50% 
Correct Answer: 50%
Let 1st person be x and 2nd person be y.
Then, x's 1 day's work = \( \Large \frac{1}{26} \)
Y's 1 days work = \( \Large \frac{1}{39} \)
x's share : y's share = \( \Large \frac{1}{26} \) : \( \Large \frac{1}{39} \)
= \( \Large \frac{3}{78} \) : \( \Large \frac{2}{78} \) = 3 : 2
Difference of ratio = 3  2 = 1
Therefore, Required percentage = \( \Large \frac{1}{2} \times 100\% \) = 50%
1st person's wages is 50% more than the 2nd person's wages. 
6). A alone can finish a work in 2 days, while B alone can finish it in 3 days. If they work together to finish it, then out of total wages of Rs.6000, what will be the 20% of A's share?
A). Rs.720 
B). Rs.350 
C). Rs.820 
D). Rs.420 
Correct Answer: Rs.720
A's 1 day's work = \( \Large \frac{1}{2} \)
B's 1 day's work = \( \Large \frac{1}{3} \)
A's share : B's share = \( \Large \frac{1}{2} \) : \( \Large \frac{1}{3} \)
= \( \Large \frac{3}{6} \) : \( \Large \frac{2}{6} \) = 3 : 2
A's share = \( \Large \frac{3}{5} \times 6000 \) = Rs.3600
Therefore, 20% of A's share = \( \Large 3600 \times \frac{20}{100} \) = Rs.720 
7). A sum of money is sufficient to pay A's wages for 21 days and B's wages for 28 days. The same money is sufficient to pay the wages of both for
A). \( \Large 24\frac{1}{2} \) days 
B). 12 days 
C). \( \Large 12\frac{1}{4} \) days 
D). 14 days 
Correct Answer: 12 days
A's 1 day's work = \( \Large \frac{1}{21} \)
B's 1 day's work = \( \Large \frac{1}{28} \)
Therefore, Same money is sufficient to pay the wages of both for
= \( \Large \frac{1}{\frac{1}{21}+\frac{1}{28}} \)
= \( \Large \frac{21 \times 28}{21+28} = \frac{21 \times 28}{49} = 3 \times 4 \) = 12 days 
8). A, B and C completed a work Costing Rs.1800. A worked for 6 days, B worked for 4 days and C worked for 9 days, If their daily wages are in the ratio of 5: 6: 4, how much amount will be received by A?
A). Rs.600 
B). Rs.500 
C). Rs.900 
D). Rs.450 
Correct Answer: Rs.600
Ratio of the wages of A, B and C = 5 : 6 : 4
A's share : B's share : C's share
= \( \Large 6 \times 5 \) : \( \Large 4 \times 6 \) : \( \Large 9 \times 4 \)
= 30 : 24 : 36  5 : 4 : 6
Therefore, A's share = \( \Large \frac{5}{15} \times 1800 \) = Rs.600 
9). A and B undertaken to do a piece of work for Rs.1200. A alone can do it in 8 days, while B can do it in 6 days. With the help of C, they complete it in 3 days, Find C's share.
A). Rs.450 
B). Rs.300 
C). Rs.150 
D). Rs.100 
Correct Answer: Rs.150
According to the question,
\( \Large \frac{1}{A} \)+\( \Large \frac{1}{B} \)+\( \Large \frac{1}{C} \) = \( \Large \frac{1}{3} \)
= \( \Large \frac{1}{8} \)+\( \Large \frac{1}{6} \)+\( \Large \frac{1}{C} \) = \( \Large \frac{1}{3} \)
= \( \Large \frac{1}{C}=\frac{1}{3} \left(\frac{1}{8}+\frac{1}{6}\right)=\frac{1}{24} \)
Therefore, Ratio in shares of A, B and C = \( \Large \frac{1}{8} \) : \( \Large \frac{1}{6} \) : \( \Large \frac{1}{24} \)
= \( \Large \frac{3}{24} \) : \( \Large \frac{4}{24} \) : \( \Large \frac{1}{24} \) = 3 : 4 : 1
Therefore, C's share = \( \Large \frac{1}{3+4+1} \times 1200 \) = Rs.150 
10). A, B and C can do a piece of work in 20, 24 and 30 days, respectively. They undertook to do the piece of work for Rs.5400. They begin the work together but B left 2 days before the completion of work and C left 5 days before the completion of work. The share of A from the assured money is
A). Rs.2700 
B). Rs.540 
C). Rs.1800 
D). Rs.600 
Correct Answer: Rs.2700
Let the number of days to complete the work be x.
According to the question,
\( \Large \frac{x}{20} \) + \( \Large \frac{x2}{24} \) + \( \Large \frac{x5}{30} \) = 1
= \( \Large \frac{6x+5 \left(x2\right)+4 \left(x5\right) }{120} = 1 \)
= \( \Large 6x +5x+4x = 120+10+20 \)
= 15x = 150
Therefore, x = 10
Therefore, Work done by A = \( \Large \frac{10}{20} = \frac{1}{2} \)
Therefore, Share of A from the assured money = \( \Large \frac{1}{2} \times 5400 \) = Rs.2700 