Question

The ratio of the speeds of two trains is 2 : 5. If the distances they travel are in the ratio 5: 9, find the ratio of the times taken by them.
a. 18:25
b. 5:4
c. 25:18
d. 1:1​

Answer 1

Answer:

v1:v2 = 2:5

S1:S2 = 5:9

v1 = S1/ t1

t1 = 5/2 sec.

v2=S2/t2

t2 = 9/5

t1:t2 = 5/2÷ 9/5

= 25:18

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Answer 2

Solution

•Let us assume the speed as 2x and 5x.

•Let us assume the distance as 5y and 9y.

We know that

${ \underline{\boxed{ \sf{T= \frac{D}{S}}}}}$

where

• S denotes speed
• D denotes distance
• T denotes time

$\sf{T_1 = \dfrac{5y}{2x}} \\ \\ \sf{T_2 = \dfrac{9y}{5x}}$

$\sf{ \pink{Ratio \: of \: time \: taken = \dfrac{T_1}{T_2}}}$

$\sf{ \to \: Ratio \: of \: time \: taken = \dfrac{\frac{5y}{2x}}{ \frac{9y}{5x}}}$

$\sf{ \to \: Ratio \: of \: time \: taken = \dfrac{5y}{2x} × \dfrac{5x}{9y}}$

$\sf{\to Ratio \: of \: time \: taken = \dfrac{25}{18}= \red{25:18 }}$

Therefore the correct option is c. 25:18

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