The document contains 10 questions and answers related to time and work problems. The questions involve calculating the time taken to complete a work by individuals or groups working alone or together. For example, question 1 asks how many days it will take 5 men and 10 women to complete a work that 10 men take 70 days and 10 women take 140 days to complete alone. The answer is provided as 70 days. Explanations for each question and answer are provided using concepts like calculating individual daily work capacities and setting up and solving equations.

1. TIME AND WORK
QUESTIONS AND
ANSWERS

2. 1) 10 Men can complete a work in 70 days and 10
women take 140 days to complete the work. How
many days will 5 men and 10 women take to
complete the work?
Ans) 70 days
Explanation:-
• One day work of one man = 1/700 ;
• One day work of one woman = 1/1400 .
• One day work of (5 men + 10 women)’s = 5/700 +
10/1400 = 1/140 + 1/140 = 1/70 .
• So 5 men and 10 women can complete the work in
70 days

3. 2) 10 Seniors and 15 Juniors together can complete a
work in 6 days. It takes 100 days for one Senior alone to
complete the work. How many days will be needed for
one Junior alone to complete the work?
Ans) 225 days
Explanation
Be focus while understanding the explanation.
• 1 Senior’s 1 day’s work = 1/100 .
• (10 Senior + 15 Junior)’s 1 day’s work = 1/6 .
• 15 Junior’s 1 day’s work = 1/6 - 10/100 =
1/6 - 1/10 = 1/15 .
• 1 Junior’s 1 day’s work = 1/225 .
• So, 1 Junior alone can complete the work in 225 days.

4. 3) 4 men and 2 boys can do a piece of work in 8 days
while 6 men and 2 boys can do the same work in 7
days. In how many days can 3 men and 3 boy do the
work?
Ans) 7 7/11
Explanation:-
: Let 1 man’s 1 day’s work = x and 1 boy’s 1 day’s work
= y.
Then, 4x+2y =1/8 and 6x+2y = 1/7.
Solving, we get: x = 1/84 and y = 1/28.
(3 men + 3 boy)’s 1 day’s work = (3x 1/84 + 3 x 1/28 )
=11/84
So, 3 men and 3 boy together can finish the work in
84/11 =7 7/11 days.

5. 4) 5 boys and 2 girls working together can finish a
work four times faster than of as one boy and one girl.
Find the working capacity ratios of boy and girl?
Ans) 2 : 1
Explanation:-
• Let us assume 1 boy’s 1 day’s work = B ;
• AND 1 girl’s 1 day’s work = G .
• According to the question,
• 5B + 2G = 4 (B + G) => B = 2G => B/G
= 2/1 .
• So the working capacity ratios of boy and girl is 2:1

6. 5) A and B together can complete a piece of work in 6
days.If A alone can complete the work in 15 days, in
how many days can B alone complete that work ?
Ans) 10
Explanation:-
(A+B ) 1 day's work = 1/6 , A's 1 day's work = 1/15
, B's 1 day's work = ?
B's 1 day's work = (A+B ) - A ,
B's 1 day's work = (1/6) - (1/15) ----> (5-2) / 30 = 3/30
= 1/10.
B's 1 day's work = 1/10
Hence , B alone can complete the work in 10 days.

7. 6) A can do a piece of work in 6 days of 8 hours each
and B can do it in 5 days of 6 hours each.How long will
they taketo do it , working together 2 4/13 hours a
day ?
Ans) 8 days
Explanation:-
A can complete the work in (6*8) = 48 , A's 1 hour's
work = 1/48.
B can complete the work in (5*6) = 30 , B's 1 hour's
work = 1/30.
(A+B) 1 hour's work = (1/48)+(1/30) = (5+8) / 240
=13/240.
Therefore Both will finish work in 240/13 hours.
Number of days of 2(4/13) hrs each =
(240/13)*(13/30) = 8 days.

8. 7) A can do a piece work in 10 days, Then what will be
the A's 1 day work ?
Ans) 1/10
Explanation:-
A can do a piece work in 10 days, A's 1 day work =
1/10.
A can do a piece work in n days, Then A's 1 day work =
1/n.

9. 8) A can do a work in 40 days.He worked for 5 days
then B finished in 21 days.In how many days can A
and B together finish the work ?
Ans) 15
Explanation:-
A's 5 days work = 5/40 = 1/8 , Remaining work = 1 -
1/8 = 7/8.
B's 21 days work = 7/8.
B's 1 day work = (1/21) * (7/8) = 1/24.
(A+B)'s 1 day work = 1/40 + 1/24 = 1/15.
A and B can do the whole work in 15 days.

10. 9) A is half good a man as B and together they finish a
job in 16 days.In how many days working alone will B
finish the job ?
Ans) 24
Explanation:-
Let B can do the work in x days and A can do the work
in 2x days.
Then, (1/x)+(1/2x) = 1/16 ------> x = (3/2)*16 =24 days.

11. 10) A pot has two holes. The first hole emptied the
pot in 9 minutes where as second hole emptied the
pot in 6 minutes. If water leaks out at a constant rate,
How much time needed to emptied the pot by both
the holes?
Ans) 3.6 minutes
Explanation:-
• 1 minute’s work of both the holes = 1/9 + 1/6
= 5/18 .
• So, both the punctures will emptied the pot in 18/5
= 3.6 minutes.

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