SSC CPO 2024 PYQ — Question 123

The correct answer is Option 4 i.e.  $\frac{25}{8} km/h$.

Let the speed of the boat be x km/h and the speed of the current be y km/h.

Speed of the boat in upstream = x - y

Speed of the boat in downstream = x + y

Let assume, 1/(x - y) = a, and 1/(x + y) = b 

According to the question,

$\frac{24}{x-y}$ + $\frac{36}{x+y}$ = 10

⇒ 12a + 18b = 5.................(1)

 $\frac{36}{x-y}$ + $\frac{24}{x+y}$ = 12

⇒ 9a + 6b = 3..............(2)

Multiplying eq (2) by 3 -

⇒ 27a + 18b = 9 ..............(3)

Subtracting eq(3) from eq(1) -

⇒  12a - 27a + 18b - 18b = 5 - 9

⇒ -15a = -4

⇒ a = 4/15

⇒ a = 1/(x + y)

So, (x + y) = 15/4....................4

put the value of a in equation 2

⇒ 9 × 4/15 + 6b = 3

⇒ 6b =  3 - 12/5

b = 1/10

So, b = 1/(x - y)

(x - y) = 10..............................5

From equations 4 and 5 we get

y = 28/5 km/h