AFCAT Model Paper 2

A boat can travel 15 km upstream and 18 km downstream in 4 hours.
It can go 18 km upstream and 15 km downstream in 4 hours 15 minutes.
Formula used:
Total Time = Distance/(Downstream speed) + Distance/(Upstream speed)
Downstream speed = Speed of the boat in still water + Speed of the stream
Upstream speed = Speed of the boat in still water – Speed of the stream
Calculation:
4 hr 15 min =

17

4

hr
Let the speed of the boat be x km/hr and speed of current be y km/hr
According to the question

15

(x–y)

+

18

(x+y)

=4
Let(x–y)=a‌and(x+y)=b
15a + 18b = 4 ---- (1)
⇒

18

(x–y)

+

15

(x+y)

= 4 hr 15 min
⇒ 18a+15b=

17

4

---(2)
Add equation (1) and equation (2)
33(a+b)=

33

4

⇒ a+b=

1

4

---(3)
Subtract equation (1) from equation (2)
3(a–b)=

1

4

⇒a–b=

1

12

---(4)
From equation (1) and equation (2)
a=

1

6

and b=

1

12

⇒ x - y = 6 ---(5)
⇒ x + y = 12 ---(6)
From equation (1) and equation (2)
x = 9 and y = 3
∴ Speed of boat in still water is = 9 km/hr