Question

A man can row a boat at the rate of 4 km/hour in still water. He takes thrice as much time in going 30 km upstream as in going 30 km downstream. Find the speed of the stream.

Or, in a competitive examination, 5 marks are awarded for each correct answer, while 2 marks are deduced for each wrong answer. Jayant answered 120 questions and got 348 marks. How many questions did he answer correctly?

Answer 1

The speed of the boat in still water is 4 km/hr.
Let the speed of the stream be ‘y’ km/hr. Then,
Speed of the boat with the stream = downstream speed = (4 + y) km/hr
Speed of the boat against the stream = Upstream speed= (4 - y) km/hr
According to question,
time taken by boat to cover 30 km downstream = t = $\frac{30}{\left(4+y\right)}\mathrm{hr}$
⇒ 30 =(4 + y)t
⇒ 30 = 4t + yt ......(i)
Time taken by boat to cover 30 km upstream = 3t = $\frac{30}{\left(4-y\right)}\mathrm{hr}$
⇒ 30 = (4 - y)3t
⇒ 30 = 12t - 3yt ......(ii)
On multiplying (i) by 3, we get:
90 = 12t + 3yt ......(iii)
On solving (ii) and (iii), we get:
t = 5 and y = 2

Hence, the speed of the stream is 2 km/hr.

OR

Let the number of correct answers be x and number of wrong answer be y. Then,
x + y = 120 .............(i)
5x - 2y = 348 .............(ii)
On multiplying (i) by 2, we get:
2x + 2y = 240 ...........(iii)
On adding (ii) and (iii), we get:
7x = 588 ⇒ x = 84
Hence, Jayant answered 84 questions correctly.