# Quantitative Aptitude – Arithmetic – TSD – A man travels by a motor boat

## Question A man travels by a motor boat down a river to his office and back. With the speed of the river unchanged, if he doubles the speed of his motor boat, then his total travel time gets reduced by 75%. The ratio of the original speed of the motor boat to the speed of the river is

A) √6 / √2
B) √7 / 2
C) 2√5 / 3
D) 3: 2

Option (B)

## Solution

As per CAT 2017 – Quantitative Aptitude – Arithmetic – Time Speed Distance, we can see that
Total travel time gets reduced by 75%. So, total travel time becomes 1/4th of the original.
So, s’(New speed) = 4s(Original speed)
Speed of boat : Speed of river = x:1
When the speed of boat is normal
Speed Upstream = x-1
Speed Downstream = x+1
Here, the distance is constant. So, average speed can be found out by the harmonic mean of two speeds = 2ab/ (a+b)
Here, average speed will be 2(x^2-1)/2x = (x^2-1)/x
When the speed of boat is doubled
Speed upstream = 2x-1
Speed downstream = 2x+1
Here, the distance is constant. So, average speed can be found out by the harmonic mean of two speeds = 2ab/(a+b)
Here, average speed will be 2(4x^2-1)/4x = (4x^2-1)/2x
Now, we know that
New speed = 4*Original speed
So,
(4x^2-1)/2x = 4(x^2-1)/x
4x^2 – 1 = 8x^2 – 8
4x^2 = 7
x = √7/2
Ratio = x:1 = √7/2
Option (B)

## CAT 2017 Questions from Quantitative Aptitude – Arithmetic

Quantitative Aptitude – Arithmetic – Time, Speed and Distance – Q1: A motorbike leaves point A at 1 pm and moves towards point B at a uniform speed. A car leaves point B at 2 pm and moves towards point A at a uniform speed which is double that of the motorbike.
Quantitative Aptitude – Arithmetic – Time, Speed and Distance – Q2: Arun drove from home to his hostel at 60 miles per hour. While returning home he drove halfway along the same route at a speed of 25 miles per hour
Quantitative Aptitude – Arithmetic – Time, Speed and Distance – Q3: In a 10 km race. A, B,and C, each running at uniform speed, get the gold, silver, and bronze medals, respectively. If A beats B by 1 km and B beats C by 1 km, then by how many metres does A beat C?
Quantitative Aptitude – Arithmetic – Time, Speed and Distance – Q4: A man leaves his home and walks at a speed of 12 km per hour, reaching the railway station 10 minutes after the train had departed.
Quantitative Aptitude – Arithmetic – Mixtures – Q1 : Consider three mixtures – the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1 : 3, and the third having water and liquid C in the ratio 1 : 4.
Quantitative Aptitude – Arithmetic – Mixtures – Q2: Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water in 9 : 4 ratio.
Quantitative Aptitude – Arithmetic – Time and Work – Q1: Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 days and are paid a total amount of Rs 1000 as remuneration.
>Quantitative Aptitude – Arithmetic – Time and Work – Q2: A person can complete a job in 120 days. He works alone on Day 1. On Day 2, he is joined by another person who also can complete the job in exactly 120 days.
Quantitative Aptitude – Arithmetic – Percentages
Quantitative Aptitude – Arithmetic – Profit and Loss
Quantitative Aptitude – Arithmetic – Pipes and Cisterns – Ques: A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in 8 hours.
Quantitative Aptitude – Arithmetic – Averages
Quantitative Aptitude – Arithmetic – Ratios

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