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ICSE Class 10 Mathematics Question 25 of 49

Multiple-Choice Questions — Question 25

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Question 25

In the given diagram (not draw to scale), railway stations A, B, C, P and Q are connected by straight tracks. Track PQ is parallel to BC. The time taken by a train travelling at 90 km/hr to reach B from A by the shortest route is :

  1. 8 minutes

  2. 12 minutes

  3. 16.8 minutes

  4. 20 minutes

In the given diagram (not draw to scale), railway stations A, B, C, P and Q are connected by straight tracks. Track PQ is parallel to BC. The time taken by a train travelling at 90 km/hr to reach B from A by the shortest route is : Maths Competency Focused Practice Questions Class 10 Solutions.
Answer

In △ APQ and △ ABC,

⇒ ∠PAQ = ∠BAC (Common angle)

⇒ ∠APQ = ∠ABC (Corresponding angles are equal)

∴ △ APQ ~ △ ABC (By A.A. axiom)

From figure,

Let AP = x km.

We know that,

Corresponding sides of similar triangle are proportional.

⇒APAB=PQBC⇒xAP+PB=2050⇒xx+18=25⇒5x=2(x+18)⇒5x=2x+36⇒5x−2x=36⇒3x=36⇒x=363⇒x=12.\Rightarrow \dfrac{AP}{AB} = \dfrac{PQ}{BC} \\[1em] \Rightarrow \dfrac{x}{AP + PB} = \dfrac{20}{50} \\[1em] \Rightarrow \dfrac{x}{x + 18} = \dfrac{2}{5} \\[1em] \Rightarrow 5x = 2(x + 18) \\[1em] \Rightarrow 5x = 2x + 36 \\[1em] \Rightarrow 5x - 2x = 36 \\[1em] \Rightarrow 3x = 36 \\[1em] \Rightarrow x = \dfrac{36}{3} \\[1em] \Rightarrow x = 12.

AB = AP + BP = 12 + 18 = 30 km.

Time = DistanceSpeed=AB90=3090=13 hr=13×60\dfrac{\text{Distance}}{\text{Speed}} = \dfrac{AB}{90} = \dfrac{30}{90} = \dfrac{1}{3} \text{ hr} = \dfrac{1}{3} \times 60 = 20 minutes.

Hence, Option 4 is the correct option.