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CAT 2024 Slot 3 — QA Question 14

Basics of TSD/ProportinalityEasy

A train travelled a certain distance at a uniform speed. Had the speed been 6 km per hour more, it would have needed 4 hours less. Had the speed been 6 km per hour less, it would have needed 6 hours more. The distance, in km, travelled by the train is

Answer & solution

  • A

    640

  • B

    780

  • C

    800

  • 720

Solution

Hard

Let speed =s=s and time =t=t, so distance D=stD=st. Form two equations from the two "what-if" scenarios (faster by 6 saves 4 h; slower by 6 costs 6 h), keeping DD constant. Solve for ss and tt, then DD.

1

Set up two equations. Distance stays stst in every scenario.

(s+6)(t−4)=st⇒ −4s+6t−24=0⇒3t−2s=12(equation A)⇒ (s−6)(t+6)=st⇒ 6s−6t−36=0⇒s−t=6(equation B)\begin{aligned} &(s+6)(t-4)=st\\ &\Rightarrow\ -4s+6t-24=0\Rightarrow 3t-2s=12\quad\text{(equation A)}\\ &\Rightarrow\ (s-6)(t+6)=st\\ &\Rightarrow\ 6s-6t-36=0\Rightarrow s-t=6\quad\text{(equation B)} \end{aligned}
2

Solve the system. From equation B, s=t+6s=t+6. Substitute into equation A.

3t−2(t+6)=12⇒ t−12=12(simplify)⇒ t=24⇒ s=t+6=30\begin{aligned} &3t-2(t+6)=12\\ &\Rightarrow\ t-12=12\quad\text{(simplify)}\\ &\Rightarrow\ t=24\\ &\Rightarrow\ s=t+6=30 \end{aligned}
3

Distance.

D=st=30×24⇒ D=720\begin{aligned} &D=st=30\times 24\\ &\Rightarrow\ D=720 \end{aligned}
720 km720\text{ km}
CAT 2024 Slot 3 QA Q14: A train travelled a certain distance at a uniform speed. Had the speed been 6 km per hour more, it would have — Solution | TheCATExam