CBSE Class 10 Maths (Basic) 2024 · Paper 430(B) · Question 36

Quadratic Equations 4 marks Very hard

The speed of a motor boat in still water is

25

km/h. For covering a distance of

40

km, the boat took

40

minutes more to go upstream than downstream. Based on the above, answer the following questions :

(i)Let the speed of the stream be $x$ km/h. Express, in terms of $x$ , the speed of the motor boat going upstream.[1]
(ii)Express the above situation in terms of a quadratic equation in $x$ .[1]
(iii)(a)Find the speed of the stream.[2]
(iii)(b) ORIf the speed of the stream is $10$ km/h, how much time will the boat take to cover $40$ km upstream ?[2]

Answer

(i) Upstream speed

= (25 - x)

km/h; (ii)

x^{2} + 120 x - 625 = 0

; (iii)(a) The speed of the stream is

5

km/h; OR (iii)(b) The boat takes

\frac{8}{3}

= 2

40

min.

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