1. A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?
A. 3.75 days
B. 4 days
C. 5 days
D. 6 days
Answer: Option A
Explanation:
[latex]\frac {1}{6}[/latex] + [latex]\frac {1}{10}[/latex] = [latex]\frac {8}{30}[/latex] = [latex]\frac {4}{15}[/latex]
[latex]\frac {15}{4}[/latex] = 3.75 days
2. A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?
A. 20 days
B. 16 days
C. 24 days
D. 28 days
Answer: Option B
Explanation:
B = [latex]\frac {1}{8}[/latex] - [latex]\frac {1}{2}[/latex] = [latex]\frac {1}{24}[/latex] => 24 days
3. A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C, they completed the work in 2 days. Find in how many days can C alone do it?
A. 10 days
B. 20 days
C. 5 days
D. 4 days
Answer: Option B
Explanation:
C = [latex]\frac {1}{2}[/latex] - [latex]\frac {1}{4}[/latex] - [latex]\frac {1}{5}[/latex] = [latex]\frac {1}{20}[/latex] => 20 days
4. A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone.
A. 2 days
B. 1 [latex]\frac {1}{2}[/latex] days
C. 3 days
D. 3 [latex]\frac {1}{2}[/latex] days
Answer: Option B
Explanation:
[latex]\frac {3}{20}[/latex] * 2 + [latex]\frac {(2 + x)}{5}[/latex] = 1
x = 1 [latex]\frac {1}{2}[/latex] days
5. A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
A. 15 days
B. 12 days
C. 10 days
D. 9 days
Answer: Option D
Explanation:
[latex]\frac {3}{12}[/latex] + [latex]\frac { (3 + x)}{16}[/latex] = 1
x = 9 days