SSC CGL Model Paper 12

Question : 59 of 100

Marks: +1, -0

A bus starts running with the initial speed of 21 km /hr and its speed increases every hour by 3 km/hr. How many hours will it take to cover a distance of 252 km ?

Validate

Solution:

The distance covered by bus in 1 hour = 21 km

\S_\n =n/2[2 a + ( n - 1) d ]

Here,

\S_\n = 252, d =3, a = 21

252 = n/2[2 × 21 + (n - 1)× 3]

⇒504 = 42n + 3 n ^2 -3 n

⇒ 3n^ 2 + 39n - 504 = 0

⇒ n ^2 + 13n -1 6 8 = 0

⇒n^ 2 + 21 n - 8 n -1 6 8 = 0

⇒n (n + 21) - 8(n + 21) = 0

⇒(n + 21) (n - 8) = 0

⇒n = 8

Hence, required time = 8 hours

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