This one is a word problem in Rates - Work and Time. Word problems test your ability to translate information given in words into mathematical expressions and equations and solve them. The gist of what is tested is the ability to translate effectively.

Question 6: Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?

- \\frac{\text{46}}{\text{9}})
- \\frac{\text{50}}{\text{9}})
- \\frac{\text{50}}{\text{11}})
- \\frac{\text{36}}{\text{7}})
- \\frac{\text{210}}{\text{41}})

@ INR

working alone at a constant rate if A takes 'a' days to complete a task, A will complete \\frac{\text{1}}{\text{a}}) of the task in a day.

A will complete \\frac{\text{1}}{\text{a}}) of the task in a day.

Therefore, in 2 days A will complete \\frac{\text{2}}{\text{a}}) of the task in a day.

Similarly, A will complete \\frac{\text{5}}{\text{a}}) of the task in 5 days.

A starts and works for 2 days. So, A will work on day 1 and day 2.

Then B will work for the next 2 days. B will work on day 3 and day 4.

A will continue for the next 2 days. i.e., on day 5 and day 6.

B will work on day 7 and day 8.

A will for the last 2 days i.e., day 9 and day 10.

Therefore, A will work on day 1, day 2, day 5, day 6, day 9, and day 10. i.e., for 6 days.

And B will work on day 3, day 4, day 7, and day 8. i.e., for 4 days.

In 6 days A will complete \\frac{\text{6}}{\text{a}}) of the task.

In 4 days B will complete \\frac{\text{4}}{\text{b}}) of the task.

With A working 6 days and B working 4 days, the task is completed.

i.e., **\\frac{\text{6}}{\text{a}}) + \\frac{\text{4}}{\text{b}}) = 1 .... eqn (1). **

Therefore, B will work on day 1, day 2, day 5, day 6, day 9, and day 10. i.e., for 6 days.

And A will work on day 3, day 4, day 7, day 8 and half a day on day 11. i.e., for 4.5 days.

In 6 days B will complete \\frac{\text{6}}{\text{b}}) of the task.

In 4 days A will complete \\frac{\text{4.5}}{\text{a}}) of the task.

With B working 6 days and A working 4.5 days, the task is completed.

i.e., **\\frac{\text{4.5}}{\text{a}}) + \\frac{\text{6}}{\text{b}}) = 1 .... eqn (2). **

\\frac{\text{6}}{\text{a}}) + \\frac{\text{4}}{\text{b}}) = 1 .... eqn (1)

\\frac{\text{4.5}}{\text{a}}) + \\frac{\text{6}}{\text{b}}) = 1 .... eqn (2)

Solving the two equations we get a = 9 days and b = 12 days.

Working together A and B will complete \\frac{\text{1}}{\text{9}}) + \\frac{\text{1}}{\text{12}})= \\frac{\text{4 + 3}}{\text{36}}) = \\frac{\text{7}}{\text{36}}) th of the task in a day.

Hence, they will complete the task in \\frac{\text{36}}{\text{7}}) days.

Try it free!

Register in 2 easy steps and

Start learning in 5 minutes!

Next Integrated (Online + Offline) GMAT Batch

Sep 21, 2020

1. 700 Level GMAT Sample Question in Inequalities & Polynomials

2. GMAT Hard Math Data Sufficiency Question

3. GMAT Data Sufficiency Question | Inequalities & Exponents

4. 700 800 Level GMAT Sample Question | Probability

5. GMAT Hard Math Question | Number Properties DS Practice

6. 700 800 Level GMAT Word Problem | Rates Problem Solving Question

7. GMAT DS Sample Question | Percentage | Ratios | Word Problem

8. GMAT 700 800 Level Question | Geometry | Area of Circles

9. GMAT Data Sufficiency | Hard Math Question | Geometry

10. GMAT Hard Math Questions | Algebra | Absolute Values Sample Question

Copyrights © 2016 - 20 All Rights Reserved by Wizako.com - An Ascent Education Initiative.

Privacy Policy | Terms & Conditions

GMAT^{®} is a registered trademark of the Graduate Management Admission Council (GMAC). This website is not endorsed or approved by GMAC.

GRE^{®} is a registered trademarks of Educational Testing Service (ETS). This website is not endorsed or approved by ETS.

SAT^{®} is a registered trademark of the College Board, which was not involved in the production of, and does not endorse this product.

Wizako - GMAT, GRE, SAT Prep

An Ascent Education Initiative

48/1 Ramagiri Nagar

Velachery Taramani Link Road.,

Velachery, Chennai 600 042. India

**Phone:** (91) 44 4500 8484

**Mobile:** (91) 95000 48484

**WhatsApp:** WhatsApp Now

**Email:** learn@wizako.com

Leave A Message