96 Views

Question : A boat can cover 120 km upstream and back in a total of 30 hours, and 25 km upstream and 40 km downstream in a total of 7 hours. How much distance will the boat cover in 16 hours in still water?

Option 1: 200 km

Option 2: 180 km

Option 3: 175 km

Option 4: 225 km


Team Careers360 25th Jan, 2024
Answer (1)
Team Careers360 26th Jan, 2024

Correct Answer: 200 km


Solution : Let the speed of the boat in still water be $x$ km/hr and the speed of the current be $y$ km/hr.
Speed downstream = $x + y$
Speed upstream = $x - y$
Now, $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$
$\frac{120}{x + y} + \frac{120}{x - y} = 30$....(1)
and$\frac{40}{x + y} + \frac{25}{x – y} = 7$ ....(2)
Multiplying equation (2) by 3, we get,
$\frac{120}{x + y} + \frac{75}{x – y} = 21$ ......(3)
Subtracting equation (3) from (1), we get,
$\frac{45}{x – y} = 9$
$⇒x - y = 5$.......(4)
Putting the value of $x - y$ in equation (2), we get,
$x + y = 20$ .......(5)
Solving these two equations, we get the values of $x$ and $y$.
$x = 12.5$ and $y = 7.5$
Distance covered by the boat in 16 hours in still water = 16 × 12.5 = 200 km
Hence, the correct answer is 200 km.

SSC CGL Complete Guide

Candidates can download this ebook to know all about SSC CGL.

Download EBook

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books