A Contractor Estimated that his 10-Man Crew Could Complete the Construction in 110 Days if There Was no Rain.

Question: A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?

1. 1.7
2. 2.7
3. 3.4
4. 5.4
5. 8

“A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. ”– is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.0

Answer
Approach Solution 1

Given: 10-man crew needs 110 days to complete the construction.

On the 61\(^{st}\) day, after 5 days of rain……: as it was raining for 5 days then they must have been working for 55 days thus completing ½ of the job, ½ is left (55 days of work for 10 men).

The contractor “hired 6 more people”: speed of construction increased 1.6 times, so the new 16- men crew needed \(\frac{55}{1.6}\approx 34.4\) days to complete the construction, but after they were hired the job was done in 100 – 60 = 40 days. Therefore, it rained for 5 days. (They needed MORE than 34 days to finish the job, so if it rained for 6 days they wouldn’t be able to finish the job in 100 (40) days.

Correct option: B

Approach Solution 2

Total work = 10 persons * 110 days = 1100 person-days

Work completed till it rained for 5 days = 10 person * 55 days = 550 person-days.

Pending work = 1100 – 550 = 550 person-days

Ideally, from 61\(^{st}\) day to 100th day, the manpower rose to 16, which means they can do a work of = 16 person * 40 days = 640 person-days

But the remaining work is only 550 person-days, so the difference is 640 – 550 = 90 person-days.

Therefore, it rained for = \(\frac{90}{16}\) = 5.625 person-days

Hence, work happened = 40 – 5.6 = 34.4 days

Hence it rained for 5 more days.

Correct option: B

Suggested GMAT Quant Questions

• A Zookeeper Counted the Heads of the Animals in a Zoo and Found it to be 80
• The Interior Angles of a Polygon are in Arithmetic Progression
• If 75 Percent of a Class Answered the First Question on a Certain Test Correctly
• 2x+3y
• If 10, 12 and ‘x’ are Sides of an Acute Angled Triangle, How Many Integer Values of ‘x’ are Possible?
• How Much Pure Alcohol Should Be Added To 400 ml of a 15% Solution To Make The Strength Of The Solution 32%?
• United Telephone charges a base rate of $10.00 for service, plus an additional charge of $0.25 per minute
• If [x] Denotes The Least Integer Greater Than or Equal to x and [x/2] = 0, Which of the Following could be the Value of x?
• A Leak in the Bottom of a Tank can Empty the Full Tank in 6 hours
• Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
• Iqbal Dealt Some Cards to Mushtaq and himself from a Full Pack of Playing Cards and Laid the Rest Aside
• Out of 7 Consonants and 4 Vowels, How Many Words of 3 Consonants and 2 Vowels Can be Formed?
• If n = \(3^8\)– \(2^8\), Which of the Following is Not a Factor of n?
• Excluding Stoppages, The Speed of a Bus is 54km/hr and Including Stoppage, It is 45km/hr
• A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively.
• A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?
• 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?
• A Merchant has 1000 kg of Sugar Part of Which He Sells at 8% Profit and The Rest at 18% Profit
• A Four Digit Number is Formed By Repeating a Two Digit Number Such as 2525, 3232, etc.
• Two Consultants, Mary and Jim, Can Type up a Report in 12.5 Hours and Edit it in 7.5 Hours.