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# GMAT QUANT, QUESTIONS: DISTANCE / RATE WORK /RATE MIXTURE PROBLEMS

Monday 2 October 2023, by

GMAT QUANT, QUESTIONS DISTANCE / RATE WORK /RATE MIXTURE PROBLEMS

DISTANCE / RATE

A man can row at a speed of 5 km/hr in still water. If he rows a certain distance upstream and back to the starting point in a river which flows at 1.5 km/hr, what is his average speed for the double journey?

A. 3.5 km/h

B. 4.55 km/h

C. 5 km/h

D. 5.5 km/h

E. 6.5 km/h

(b)

Seb’s watch gains 5 seconds in every 3 hours, whereas Lewis’ watch loses 10 seconds in every 2 hours. If both watches are set to the correct time at 1 a.m. Sunday, then at what earliest time they will have a difference of 9 minutes among them?

A. 7 a.m. Wednesday

B. 10 a.m. Wednesday

C. 7 p.m. Wednesday

D. 10 p.m. Wednesday

E. 7 a.m. Thursday

(b)

A bus made a roundtrip journey from Madison towards Chicago, which is 240 km away. In the onward journey the bus divided the journey time in 3 equal blocks. Started at 50 kph, it took stoppages after every block and increased its speed by 10 kph after every stoppage. At Chicago, it took a halt of 7 hrs 44 minutes. The return journey was divided into two equidistant blocks, covered at 45 kph and 75 kph respectively. Find by what amount the average speed of the whole journey of the bus is less than the sum of the average speeds of onward and return journey;

A. 75 kph

B. 86.25 kph

C. 97.5 kph

D. 105 kph

E. 120 kph

(b)

Two runners, P and Q, competed in a race of 400 m. P ran at a constant speed of 5 strides in every 2 seconds, covering 10 m in that span. Q started at a constant speed. After running for 1 minute, Q increased its speed by 1 stride per second and finally finished the race at the same time with P. What is Q’s initial speed in kph if Q covered 4 m in every stride?

A. 10 kph

B. 11.5 kph

C. 12.8 kph

D. 13.6 kph

E. 14.4 kph

(E)

Three bodies A, B and C start moving around a circular track of length 60m from the same point simultaneously in the same direction at speeds of 3 m/s, 5 m/s and 9 m/s respectively. When will they meet for the first time after they started moving?

A. 30 seconds

B. 60 seconds

C. 15 seconds

D. 10 seconds

E. 25 seconds

(A)

A ship is travelling between two port cities with a speed such that it will reach its destination on time. After covering 25% of the distance, the ship faces an emergency and returns to its starting point with a different speed v. It then resumes travelling towards its destination without any further delay with the same speed v. By what percentage is v more than the original speed, if the ship reaches its destination in time?

A. 33.33

B. 50

C. 66.67

D. 75

E. 87.5

(C)

WORK / RATE

A group of 4 construction workers, all working at the same constant rate, can build a wall in 20 hours. At the beginning of the day, only 2 construction workers are working on the wall, but after every hour, 2 more workers join the others. When the wall is completed, how many construction workers will be working? (Assume all workers individually work at the same constant rate.)

(A) 8

(B) 10

(C) 13

(D) 16

(E) 18

(E)

Running at their respective constant rates, Machine X takes 2 days longer to produce w widgets than Machine Y. At these rates, if the two machines together produce (5/4)w widgets in 3 days, how many days would it take Machine X alone to produce 2w widgets?

(A) 4

(B) 6

(C) 8

(D) 10

(E) 12

(E)

The days taken to built a wall individually by each of A, B, C, D and E is 20 days, 15 days, 12 days, 10 days and 6 days. They divide themselves into two teams such that the days taken by the two teams to finish the work are in the ratio 1.5 : 4.5. Find the team that finishes earlier.

A. A, B

B. C, D, E

C. B, C

D. A, D, E

E. B, E

(B)

A is twice as efficient as B and B is thrice as efficient as C. If all three together can complete a work in 10 days, find the difference in the number of days taken to complete the work when A and B work together and when B and C work together.

A. 25

B. 125/6

C. 125/7

D. 125/8

E. 125/9

(E)

A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump A or pump B or both start working until the tank is full. On Monday, A alone completed filling the tank at 8 pm. On Tuesday, B alone completed filling the tank at 6 pm. On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. At what time was the tank filled on Thursday if both pumps were used simultaneously all along?

A. 4 : 12 PM

B. 4 : 24 PM

C. 4 : 36 PM

D. 4 : 46 PM

E. 4 : 48 PM

(B)

MIXTURE PROBLEMS

Rice of two different varieties A and B are mixed together, by a seller, in the ratio of 4: 7. Upon selling the mixture at the price of $17 per kg, the seller incurred a loss of 15%. If the cost price of B is $22 per kg, what is the cost price per kg of A?

A. 15

B. 16.5

C. 17.75

D. 18

E. 19

(B)

A vessel contains milk and water in the ratio 3:2. The volume of the contents is increased by 50% by adding water to this. From this solution 30 litre of the mixture is withdrawn and then replaced with water. The resultant ratio of milk to water in the final solution is 3:7. Find the original volume of the solution?

A. 65 L

B. 75 L

C. 77 L

D. 80 L

E. 82 L

(D)

Eight litres of wine is drawn from a cask full of wine and is replaced with water. The operation is repeated three more times. The ratio of the quantity of wine left in cask to that of water is 16:65. How much wine did the cask originally hold?

A. 18 litres

B. 24 litres

C. 32 litres

D. 42 litres

E. 60 litres

(B)

A jar contains a mixture of 175 ml water and 700 ml alcohol. Randy takes out 10% of the mixture and substitutes it by water of the same amount. If the process is repeated once again, what will be the percentage of water in the mixture ?

A. 20.5

B. 25.4

C. 29.5

D. 30.3

E. 35.2

(E)

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