CUET UG 2025 — General Test Arithmetic

Two trains running in opposite directions cross a stationary lady standing at point F in 26 seconds and 21 seconds respectively. The two trains cross each other in 24 seconds.

Let the speeds of Train 1 and Train 2 be $v_1$v1​ and $v_2$v2​ respectively.

Let the lengths of Train 1 and Train 2 be $L_1$L1​ and $L_2$L2​ respectively.

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When a train passes a stationary person, the train travels a distance equal to its own length.

For Train 1:

$$L_1 = v_1 \times 26$$L1​=v1​×26

$L_1 = 26v_1$L1​=26v1​ ... (1)

For Train 2:

$$L_2 = v_2 \times 21$$L2​=v2​×21

$L_2 = 21v_2$L2​=21v2​ ... (2)

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When the two trains cross each other while moving in opposite directions, their relative speed is $v_1 + v_2$v1​+v2​.

The combined distance covered is $L_1 + L_2$L1​+L2​ in 24 seconds.

$L_1 + L_2 = (v_1 + v_2) \times 24$L1​+L2​=(v1​+v2​)×24 ... (3)

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Substituting (1) and (2) into (3):

$$26v_1 + 21v_2 = 24(v_1 + v_2)$$26v1​+21v2​=24(v1​+v2​)

$$26v_1 + 21v_2 = 24v_1 + 24v_2$$26v1​+21v2​=24v1​+24v2​

$$26v_1 - 24v_1 = 24v_2 - 21v_2$$26v1​−24v1​=24v2​−21v2​

$$2v_1 = 3v_2$$2v1​=3v2​

$$\dfrac{v_1}{v_2} = \dfrac{3}{2}$$v2​v1​​=23​

Therefore, the ratio of the speeds of the two trains is $3:2$3:2.