# Time and Work Quiz Set 008

### Question 1

A can do a piece of work in 46 days. B is 15% more efficient than A. In how many days will they complete the work if they work together?

A

\$13{31/33}\$ days.

B

\$13{32/33}\$ days.

C

14 days.

D

\$21{17/43}\$ days.

Soln.
Ans: a

Let us first calculate the one day work of B. One day work of A is given as \$1/46\$. If B is 15% efficient, then one day work of B is \$1/46\$ × \$115/100\$ = \$1/40\$. Putting x = 46 and y = 40 in the shortcut method, we get \${xy}/{x + y}\$ = \${1840/86}\$, which is same as: \$21{17/43}\$.

### Question 2

A, B and C complete a work in 19, 9 and 11 days respectively. All three of them start the work together, but A leaves the work after 5 days. In how many days will the work be completed?

A

\$3{123/190}\$ days.

B

\$4{123/190}\$ days.

C

\$5{123/190}\$ days.

D

\$6{123/190}\$ days.

Soln.
Ans: a

Use the shortcut formula. If A, B, C can independently complete the job in x, y and z days, and A leaves after n days, the work is completed in \${yz}/{y + z}\$ × \$(1 - n/x)\$ days. Putting the various values x = 19, y = 9, z = 11, n = 5, and simplifying, we get \${693/190}\$, which is same as: \$3{123/190}\$.

### Question 3

A, B and C complete a work in 9, 16 and 19 days respectively. All three of them start the work together, but A leaves the work after 1 days, and B leaves the work after 7 days. In how many days will the work be completed?

A

\$8{83/144}\$ days.

B

\$9{83/144}\$ days.

C

\$10{83/144}\$ days.

D

\$11{83/144}\$ days.

Soln.
Ans: a

Use the shortcut formula. If A, B, C can independently complete the job in x, y and z days, and A leaves after n days, and B after m days, the work is completed in z × \$(1 - n/x - m/y)\$ days. Putting the various values x = 9, y = 16, z = 19, n = 1, m = 7, and simplifying, we get \${1235/144}\$, which is same as: \$8{83/144}\$.

### Question 4

A can do a piece of work in 11 days. B is 10% more efficient than A. In how many days will they complete the work if they work together?

A

\$5{5/21}\$ days.

B

\$5{2/7}\$ days.

C

\$5{1/3}\$ days.

D

\$5{8/21}\$ days.

Soln.
Ans: a

Let us first calculate the one day work of B. One day work of A is given as \$1/11\$. If B is 10% efficient, then one day work of B is \$1/11\$ × \$110/100\$ = \$1/10\$. Putting x = 11 and y = 10 in the shortcut method, we get \${xy}/{x + y}\$ = \${110/21}\$, which is same as: \$5{5/21}\$.

### Question 5

Mr. X can finish a task in 14 days. Mr. Y can do the same work in 10 days. What is the ratio of the efficiencies of X : Y?

A

\${5/7}\$.

B

\$1{5/7}\$.

C

\${5/6}\$.

D

\${3/4}\$.

Soln.
Ans: a

The efficiency of X is \$100/14\$%, and the efficiency of Y is \$100/10\$%, so the ratio will be \$10/14\$ 