A Can Complete a Project in 20 days and B Can Complete the GMAT Problem Solving

Question: A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, how many days will the project be completed?

(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 16 days
(E) 12 days

Answer: A

Solution and Explanation:

Approach Solution 1:

Given that A can finish a project in the question in 20 days, B can do the identical project in 30 days. A and B are believed to have started working on the same project together, however, A left the project 10 days before it was finished. How many days will it take to complete the project is a question that has been raised.

The rate of A is 1/20 job per day;
The rate of B is 1/30 job per day.

Say they need t days to complete the project.

According to the stem we have that B works for all tt days and A works only for t−10 days, thus
1/20∗(t−10)+1/30∗t = 1 --> t=18 days.

Answer: A.

Correct Answer: A

Approach Solution 2:

Given in the question that A can complete a project in 20 days,
B can complete the same project in 30 days. It is said that A and B start working on the same project together, but A quits 10 days before the project is completed. It has been asked how many days it will take to complete the project.

Assume to total work to be 60 Units ( LCM of 20 & 30)
A does 3 units per day ( =60/20)
B does 2 units per day ( =60/30)
B works for 10 days alone work done = 2*10 = 20 units
A and B work together for the rest of the time
work left = 40 units
A and b together to 5 units per day ( 2+3 = 5)
days required to do 40 units = 40/5 = 8

Total = 10+8 = 18

Correct Answer: A

Approach Solution 3:

In the 10 days that B worked alone, 10*1/30 = 1/3 of the job was done, and 2/3 of the job was left to be done by A and B together.

Rate * Time = Job Done
--> (1/20+1/30) * Time = ⅔
--> Time=8. So, they worked together for 8 days, which means that the total time is 10 + 8 = 18 days.

Hence, it is the correct answer.

Correct Answer: A

Suggested GMAT Problem Solving Samples

• The product of the first 10 prime numbers is closest to which of the following? GMAT problem solving
• There is a 120 liter mixture of alcohol and water. The ratio of alcohol to water is 7 : 5 GMAT problem solving
• An equilateral triangle ABC is inscribed in square ADEF, forming three right triangles GMAT problem solving
• A Furniture Store Sells Only Two Models of Desks, Model A and Model B. The Selling Price of Model A is $120 GMAT problem solving
• A contractor combined x tons of a gravel mixture that contained 10 percent gravel G GMAT problem solving
• There are 100 Apples in a Bag of which 98% are Green and Rest are Red GMAT problem solving
• How many litres of a 90% solution of concentrated acid needs to be mixed with a 75% solution GMAT problem solving
• Jug Contains Water And Orange Juice In The Ratio 5:7 . Another Jug Contains Water And Orange J GMAT problem solving
• The number of ways in which 8 different flowers can be seated to form a garland so that 4 particular flowers are never separated GMAT problem solving
• A train travels from Albany to Syracuse, a distance of 120 miles, at an average rate of 50 miles per hour GMAT problem solving
• The hexagon ABCDEF is regular. That means all its sides are the same length and all its interior angles are the same size. GMAT problem solving
• y varies directly as x and when x = 6, y = 24. What is the value of y, when x = 5? GMAT problem solving
• If k is an Integer and 2 < k < 7, for How Many Different Values of k is There a Triangle With Sides of Lengths 2, 7, and k? GMAT problem solving
• How many factors does 36^2 have? GMAT problem solving
• A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively GMAT problem solving
• Walking at 6/7 th of his usual speed, a man is 25 min too late GMAT problem solving
• An Inlet Pipe can Fill in an Empty Cistern in 30 minutes Whereas a leak in the Bottom of the Cistern can Empty a Filled Tank in 40 minutes GMAT problem solving
• A milkman cheats his customers by adding water to the milk he sells GMAT problem solving
• if 80 lamps can be lighted, 5 hours per day for 10 days for $21.25, then the number of lamps, GMAT problem solving
• Few of the corporate contributions to the earthquake relief fund, aside from Pterocom GMAT problem solving