Answer the following practice questions on time and work:
A, B and C can complete a work in 10, 12 and 15 days respectively. They started the work together. But A left the work before 5 days of its completion. B also left the work 2 days after A left. In how many days was the work completed?
A can complete a piece of work in 10 days, B in 15 days and C in 20 days. A and C worked together for two days and then A was replaced by B. In how many days, altogether, was the work completed ?
A can do a piece of work in 18 days and B in 12 days. They began the work together, but B left the work 3 days before its completion. In how many days, in all, was the work completed?
(a) 12 days
(b) 10 days
(c) 9.6 days
(d) 9 days
(e) 18 days
Answer for this question on Time and Work is (d)
Let the work be finished in x days.
According to the question,
A worked for x days while B worked for (x – 3) days
A and B together can complete a work in 12 days. A alone can complete in 20 days. If B does the work only half a day daily, then in how many days A and B together will complete the work ?
(a) 10 days
(b) 20 days
(c) 11 days
(d) 15 days
(e) 25 days
Answer for the practice question on Time and Work is (d)
B’s 1 day’s work = \(\displaystyle \frac{1}{{12}}-\frac{1}{{20}}=\frac{{5-3}}{{60}}=\frac{1}{{30}}\)
B’s \(\displaystyle \frac{1}{2}\) day’s work = \(\displaystyle \frac{1}{{60}}\)
(A + B)’s 1 day’s work = \(\displaystyle \frac{1}{{20}}+\frac{1}{{60}}=\frac{{3+1}}{{60}}=\frac{1}{{15}}\)
[ B works for half day daily]
Hence, the work will be completed in 15 days
If 6 men and 8 boys can do a piece of work in 10 days and 26 men and 48 boys can do the same in 2 days, then the time taken by 15 men and 20 boys to do the same type of work will be :
(a) 5 days
(b) 4 days
(c) 6 days
(d) 7 days
(e) 9 days
Answer for the practice question on Time and Work is (b)
According to question,
(6M + 8B) × 10 = (26M + 48B) × 2
60M + 80B = 52M + 96B or, 1M = 2B
15M + 20B = (30 + 20)B
= 50 boys and 6M + 8B
= (12 + 8) boys = 20 boys
20 boys can finish the work in 10 days
Therefore, 50 boys can finish the work in \(\displaystyle \frac{{20\times 10}}{{50}}days=4days\)
5 men can do a piece of work in 6 days while 10 women can do it in 5 days. In how many days can 5 women and 3 men do it ?
(a) 4 days
(b) 5 days
(c) 6 days
(d) 8 days
(e) 10 days
Answer for the practice question on Time and Work is (b)
5 × 6 men = 10 × 5 women
\(\displaystyle \Rightarrow \) 3 men = 5 women
Therefore, 5 women + 3 men = 6 men
5 men complete the work in 6 days
Hence, 6 men will complete the work in \(\displaystyle \frac{{5\times 6}}{6}=5days\)
Alternate Method :
Here, A = 5, a = 6
B = 10, b = 5
\(\displaystyle {{A}_{1}}=3,{{B}_{1}}=5\)
Time taken = \(\displaystyle \frac{1}{{\frac{{{{A}_{1}}}}{{A\times a}}+\frac{{{{B}_{1}}}}{{B\times b}}}}=\frac{1}{{\frac{3}{{5\times 6}}+\frac{5}{{10\times 5}}}}=\frac{1}{{\frac{1}{{10}}+\frac{1}{{10}}}}=5days\)
If 3 men or 6 women can do a piece of work in 16 days, in how many days can 12 men and 8 women do the same piece of work?
(a) 4 days
(b) 5 days
(c) 3 days
(d) 2 days
(e) 8 days
Answer for the practice question on Time and Work is (c)
3m = 6w
\(\displaystyle \Rightarrow \) 1m = 2w
12m + 8w = (12 × 2w) + 8w = 32w
Therefore, 6 women can do the work in 16 days.
\(\displaystyle \Rightarrow \) 32 women can do the work in \(\displaystyle \frac{{16\times 6}}{{32}}=3days\)
Alternate Method :
Here, A = 3, B = 6, a = 16
\(\displaystyle {{A}_{1}}=12,{{B}_{1}}=8\)
Time taken = \(\displaystyle \frac{{a(A\times B)}}{{{{A}_{1}}B+{{B}_{1}}A}}=\frac{{16(3\times 6)}}{{12\times 6+8\times 3}}=\frac{{16\times 18}}{{96}}=3days\)
