If a man goes to the office from his home with a speed 12 km/hr, he reaches the office 1 hour late. When he goes to the office with a speed of 16 km/hr, he reaches the office 1 hour early then find the distance between the home and the office (in kilo meters).?

Question

If a man goes to the office from his home with a speed 12 km/hr, he reaches the office 1 hour late. When he goes to the office with a speed of 16 km/hr, he reaches the office 1 hour early then find the distance between the home and the office (in kilo meters).?

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LohaHridoy

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2025-01-04 04:42

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 2 : 96

Given:

Initial speed of man = 12 km/hr

Final speed of man = 16 km/hr

Concept used:

The distance traveled will be the same in both case because the man returns to the same place from he went.

Formula used:

Distance = Speed × Time

Calculation:

Let the distance between the home and the office be D.

Let the time taken to reach the office be t.

According to the 1^st condition,

D = 12(t + 1)

⇒ D = 12t + 12 ----(1)

According to the 2^nd condition,

D = 16(t - 1)

⇒ D = 16t - 16 ----(2)

From equation (1) and equation (2),

12t + 12 = 16t - 16

⇒ 16t - 12t = 12 + 16

⇒ 4t = 28

⇒ t = 28/4

⇒ t = 7

Put the value of t in equation (1),

D = 12 × 7 + 12

⇒ D = 84 + 12

⇒ D = 96

∴ The distance is 96 kilo meters.

Shortcut Trick

Formula used:

D = × (time difference)

where, S₁ = Initial speed of the man.

S₂ = Final speed of the man.

Calculation:

Let the time taken to reach the office be t.

Time difference = (t + 1) - (t - 1)

⇒ Time difference = (t + 1 - t + 1)

⇒ Time difference = 2 hours

D = (12 × 16)/(16 - 12) × 2

⇒ D = (12 × 16)/4 × 2

⇒ D = 96

∴ The distance is 96 kilo meters.