SSC GD Constable 6 Feb 2025 Shift 1 Paper

Section: Elementary Mathematics

Question : 52 of 80

Marks: +1, -0

If a train runs at 40 km/hr, it reaches its destination late by 10 min, but if it runs by 45 km/hr, it is late by 4 min. The correct time for the train to complete the journey is:

45 min
24 min
34 min
44 min

Validate

Solution:

Time

=

Distance

\div

Speed
Difference in time = Late time difference

\;\text " ⇒ "\; \;\text " Distance "\;=\;\text " Speed "\; \;\text " × "\; \;\text " Time "\;

Calculations:
Let the correct time for the train to complete the journey be T hours.
At

S_1

, total time taken

=T+1 \/ 6

S _2

, total time taken

= T +1 \/ 15

Distance covered at both speeds is the same:

\;⇒ \;\text " Distance "\;=S_1 ×(T+1 \/ 6)=S_2 ×(T+1 \/ 15)

\;⇒ 40 ×(T+1 \/ 6)=45 ×(T+1 \/ 15)

\;⇒ 40 T+(40 × 1 \/ 6)=45 T+(45 × 1 \/ 15)

\;⇒ 40 T+40 \/ 6=45 T+45 \/ 15

\;⇒ 40 T+20 \/ 3=45 T+3

\;⇒ 20 \/ 3-3=45 T-40 T

\;⇒ 20 \/ 3-9 \/ 3=5 T

\;⇒ 11 \/ 3=5 T

\;⇒ T=11 \/(3 × 5)

\;⇒ T=11 \/ 15 hr

Convert T to minutes:

⇒ T=(11 \/ 15) × 60

⇒ T=44 min

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