Question

A train has 5 coaches attached to an engine. 180 seats are available in all the coaches.

There are 30 seats in the $1^{st}$ coach. The number of seats in the $2^{nd}$ coach is twice the number of seats in the $1^{st}$ coach. The ratio of the number of seats in the $3^{rd}$, $4^{th}$, and $5^{th}$ coaches is 2:3:4.

Find the minimum number of seats in a coach.

• A. 30
• B. 20
• C. 15
• D. 40

Answer 1

The correct option is B 20

Total number of seats = 180

Number of seats in the $1^{st}$ coach = 30

Number of seats in the $2^{nd}$ coach = 2 × 30 = 60

Remaining seats = 180 – (30 + 60) = 90

Ratio of the number of seats in the $3^{rd}$, $4^{th}$, and $5^{th}$ coaches = 2:3:4

Sum of ratio = 2 + 3 + 4 = 9

Number of seats in the $3^{rd}$ coach
$=90\times \frac{2}{9}$
$⟹10\times 2=20$

Number of seats in the $4^{th}$ coach
$=90\times \frac{3}{9}$
$⟹10\times 3=30$

Number of seats in the $5^{th}$ coach
$=90\times \frac{4}{9}$
$⟹10\times 4=40$

$1^{st}$ coach = 30
$2^{nd}$ coach = 60
$3^{rd}$ coach = 20
$4^{th}$ coach = 30
$5^{th}$ coach = 40

The minimum number of seats in a coach is 20.