maths 8 class time and work icse
Answers
Question 1: A can do a piece of work in 15 days while B can do it in 10 days. How long will they take together to do it?
Answer:
A’s 1 Day = \frac{1}{15}
B’s 1 Day work = \frac{1}{10}
A’s + B’s 1 Day work = (\frac{1}{15}+\frac{1}{10})=\ \frac{5}{30}=\ \frac{1}{6}
Therefore both can finish the work in 6 Days.
Question 2: A, B and C can do a piece of work in 12 days, 15 days and 10 days respectively. In what time will they all together finish it?
Answer:
A’s 1 Day = \frac{1}{12}
B’s 1 Day work = \frac{1}{15}
C’s 1 Day work = \frac{1}{10}
(A’s + B’s + C’s) 1 Day work = (\frac{1}{12} +\frac{1}{15} + \frac{1}{10}) = \frac{15}{60} = \frac{1}{4}
Therefore all three can finish the work in 4 Days.
Question 3: A and B together can do a piece of work in 35 days, while A alone can do it in 60 days. How long would B alone take to do it?
Answer:
A’s 1 Day = \frac{1}{60}
B’s 1 Day work = \frac{1}{x}
(A’s + B’s) 1 Day work = (\frac{1}{60} + \frac{1}{x} ) = \frac{1}{35}
Solving for x = 84 Days
Question 4: A can do a piece of work in 20 days while B can do it in 15 days. With the help of C, they finish the work in 5 days. In what time would C alone do it?
Answer:
A’s 1 Day = \frac{1}{20}
B’s 1 Day work = \frac{1}{15}
C’s 1 Day work = \frac{1}{x}
(A’s + B’s + C’s) 1 Day work = (\frac{1}{20} +\frac{1}{15} + \frac{1}{x} ) = \frac{1}{5}
Solving for x = 12 Days
Question 5: A can do a piece of work in 12 days and B alone can do it in 16 days. They worked together on it for 3 days and then A left. How long did B take to finish the remaining work?
Answer:
A’s 1 Day = \frac{1}{12}
B’s 1 Day work = \frac{1}{16}
(A’s + B’s) 1 Day work = (\frac{1}{12} +\frac{1}{16} ) = \frac{7}{48}
The amount of work that is completed in 3 days = \frac{3\times7}{48} = \frac{7}{16}
Amount of work left for B to complete = 1 - \frac{7}{16} = \frac{9}{16}
Therefore the number of days that B will take to finish the work = \frac {\frac{9}{16}} {\frac{1}{16} } = 9 days
Question 6: A can do \frac{1}{4} of a work in 5 days, while B can do \frac{1}{5} of the work in 6 days. In how many days can both do it together?
Answer:
If A can do \frac{1}{4} of a work in 5 days, then A can do the entire work in 20 days.
Therefore A’s 1 Day Work = \frac{1}{20}
If B can do \frac{1}{5} of a work in 6 days, then B can do the entire work in 30 days.
Therefore B’s 1 Day Work = \frac{1}{30}
(A’s + B’s) 1 Day work = (\frac{1}{20} +\frac{1}{30} ) = \frac{1}{12}
Therefore both can do the work in 12 days.
Question 7: A can dig a trench in 6 days while B can dig it in 8 days. They dug the trench working together and received 1120 for it. Find the share of each in it.
Answer:
A’s 1 Day = \frac{1}{6}
B’s 1 Day work = \frac{1}{8}
Therefore the ratio of work = \frac {\frac{1}{6}} {\frac{1}{8} } = \frac{8}{6}
Therefore A’s share = \frac{8}{14} \times 1120 = 640
Therefore B’s share = \frac{6}{14} \times 1120 = 480
Question 8: A can mow a field in 9 days; B can mow it in 12 days while C can mow it in 8 days. They all together mowed the field and received 1610 for it. How will the money be shared by them?
Answer:
A’s 1 Day = \frac{1}{9}
B’s 1 Day work = \frac{1}{12}
C’s 1 Day work = \frac{1}{18}
Therefore the ratio of their one day’s work = \frac{1}{9} \colon \frac{1}{12} \colon \frac{1}{18} = 8 \colon 6 \colon 9
Hence A’s share = \frac{8}{23} \times 1120 = 560
Hence A’s share = \frac{6}{23} \times 1120 = 420
Hence A’s share = \frac{9}{23} \times 1120 = 630
Answer:
Question 1:
A can do a piece of work in
15 days while
B can do it in
10 days. How long will they take together to do it?
Answer:
A’s 1 Day
=
\frac{1}{15}
B’s 1 Day work
=
\frac{1}{10}
A’s + B’s 1 Day work =
(
\frac{1}{15}
+
\frac{1}{10}
)=
\frac{5}{30}
=
\frac{1}{6}
Therefore both can finish the work in 6 Days.
\\
Question 2:
A, B and
C can do a piece of work in
12 days,
15 days and
10 days respectively. In what time will they all together finish it?
Answer:
A’s 1 Day
=
\frac{1}{12}
B’s 1 Day work
=
\frac{1}{15}
C’s 1 Day work =
\frac{1}{10}
(A’s + B’s + C’s) 1 Day work
=
(
\frac{1}{12}
+
\frac{1}{15}
+
\frac{1}{10}
) =
\frac{15}{60}
=
\frac{1}{4}
Therefore all three can finish the work in 4 Days.
\\
Question 3:
A and
B together can do a piece of work in
35 days, while
A alone can do it in
60 days. How long would
B alone take to do it?
Answer:
A’s 1 Day
=
\frac{1}{60}
B’s 1 Day work
=
\frac{1}{x}
(A’s + B’s) 1 Day work
=
(
\frac{1}{60}
+
\frac{1}{x}
) =
\frac{1}{35}
Solving for
x = 84 Days
\\
Question 4:
A can do a piece of work in
20 days while
B can do it in
15 days. With the help of
C , they finish the work in
5 days. In what time would
C alone do it?
Answer:
A’s 1 Day
=
\frac{1}{20}
B’s 1 Day work
=
\frac{1}{15}
C’s 1 Day work
=
\frac{1}{x}
(A’s + B’s + C’s) 1 Day work
=
(\frac{1}{20}
+
\frac{1}{15}
+
\frac{1}{x}
) =
\frac{1}{5}
Solving for
x = 12 Days
\\
Question 5:
A can do a piece of work in
12 days and
B alone can do it in
16 days. They worked together on it for
3 days and then
A left. How long did
B take to finish the remaining work?
Answer:
A’s 1 Day
=
\frac{1}{12}
B’s 1 Day work
=
\frac{1}{16}
(A’s + B’s) 1 Day work
=
(
\frac{1}{12}
+
\frac{1}{16}
) =
\frac{7}{48}
The amount of work that is completed in 3 days
=
\frac{3\times7}{48}
=
\frac{7}{16}
Amount of work left for B to complete
=
1 -
\frac{7}{16}
=
\frac{9}{16}
Therefore the number of days that B will take to finish the work
=
\frac {\frac{9}{16}} {\frac{1}{16} } = 9 days
\\
Question 6:
A can do
\frac{1}{4} of a work in
5 days, while
B can do
\frac{1}{5} of the work in
6 days. In how many days can both do it together?
Answer:
If A can do
\frac{1}{4} of a work in
5 days, then A can do the entire work in
20 days.
Therefore A’s 1 Day Work
=
\frac{1}{20}
If B can do
\frac{1}{5} of a work in
6 days, then B can do the entire work in
30 days.
Therefore B’s 1 Day Work
=
\frac{1}{30}
(A’s + B’s) 1 Day work
=
(\frac{1}{20}
+
\frac{1}{30}
) =
\frac{1}{12}
Therefore both can do the work in
12 days.
\\
Question 7:
A can dig a trench in
6 days while
B can dig it in
8 days. They dug the trench working together and received
1120 for it. Find the share of each in it.
Answer:
A’s 1 Day
=
\frac{1}{6}
B’s 1 Day work
=
\frac{1}{8}
Therefore the ratio of work
=
\frac {\frac{1}{6}} {\frac{1}{8} } = \frac{8}{6}
Therefore A’s share
=
\frac{8}{14}
\times 1120 = 640
Therefore B’s share
=
\frac{6}{14}
\times 1120 = 480
\\
Question 8:
A can mow a field in
9 days;
B can mow it in
12 days while
C can mow it in
8 days. They all together mowed the field and received
1610 for it. How will the money be shared by them?
Answer:
A’s 1 Day
=
\frac{1}{9}
B’s 1 Day work
=
\frac{1}{12}
C’s 1 Day work
=
\frac{1}{18}
Therefore the ratio of their one day’s work
=
\frac{1}{9}
\colon
\frac{1}{12}
\colon
\frac{1}{18}
= 8 \colon 6 \colon 9
Hence A’s share
=
\frac{8}{23}
\times 1120 = 560
Hence A’s share
=
\frac{6}{23}
\times 1120 = 420
Hence A’s share
=
\frac{9}{23}
\times 1120 = 630
\\
Question 9:
A and
B can do a piece of work in
30 days;
B and
C in
24 days;
C and
A in
40 days. How long will it take them to do the work together? In what time can each finish it, working alone?
Answer:
(A’s + B’s) 1 Day work
=
\frac{1}{30}
(B’s + C’s) 1 Day work
=
\frac{1}{24}
(C’s + D’s) 1 Day work
=
\frac{1}{40}
Adding the above three
2\times(A + B + C) day work =
(\frac{1}{30}
+
\frac{1}{24}
+
\frac{1}{40}
) =
\frac{1}{10}
Therefore if they all work together, they will take 20 days to finish the work.
\\
Question 10:
A can do a piece of work in
80 days. He works at it for
10 days and then
B alone finishes the remaining work in
42 days. In how many days could both do it?
Answer:
A’s 1 Day
=
\frac{1}{80}
Work finished by A in 10 days
=
\frac{1}{80} \times
10 =
\frac{1}{8}
B finished the remainder of work
(1 -
\frac{1}{8}
) =
\frac{7}{8} in
42 days
Therefore 1 Days work for B
=
\frac{\frac{7}{8}}{42}
=
\frac{1}{48}
Hence B can do the work in 48 days
(A’s + B’s) 1 Day work
=
(
\frac{1}{80}
+
\frac{1}{48}
)=
\frac{1}{30}
Therefore both can do the work in 30 days.