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A mouse is running at the speed of 15 m/min. After 12 min a cat saw him and started running to catch the mouse at the speed of 16 m/min. How much time will it take to catch the mouse if the cat can boost his speed by 1 m/min in every 5 min?

A mouse is running at the speed of 15 m/min. After 12 min a cat saw him and started running to catch the mouse at the speed of 16 m/min. How much time will it take to catch the mouse if the cat can boost his speed by 1 m/min in every 5 min? Correct Answer <span style="font-size: 12pt; line-height: 115%; font-family: Calibri, sans-serif;">40 min</span>

Distance covered by mouse in 10 min = speed of mouse × time = 15 × 12 = 180 meter

Cat needs to cover the distance of 180 meters to catch the mouse.

Relative speed of Cat and mouse for first 5 min = 16 – 15 = 1 m/min

Relative speed of Cat and mouse for next 5 min = (16 + 1) – 15 = 2 m/min

Relative speed of Cat and mouse for next 5 min = (16 + 2) – 15 = 3 m/min and so on.

So, Distance covered in first 5 min = 1 × 5 = 5 meters

Distance covered in next 5 min = 2 × 5 = 10 meters

Distance covered in next 5 min = 3 × 5 = 15 meters and so on.

Total distance to be covered = 180 meter

So, we’ll use Arithmetic progression and first term of it a = 5 m, d = 10 – 5 = 5 and Sn = 180 m

⇒ Sn = n/2 ×

⇒ 180 = n/2 ×

⇒ 360 = n ×

⇒ n2 + n – 72 = 0

⇒ (n – 9) (n + 8) = 0

⇒ n = 8 and n = – 9

Here, n = 8 shows no. of time speed changes.

∴ Total time to catch the mouse = 8 × 5 min = 40 min

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