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### 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?

This Blog Post/Article "Time and Work Quiz Set 008" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2020-02-07. Published on: 2016-05-03