A shopkeeper sold an article for ? 6750 after giving a discount of 10% on the labelled price. He would have earned a profit of 50%, had there been no discount. What was the actual percentage of profit earned?

(A's speed) : (B's speed) = √b : √a = √16 : √9 = 4 : 3.

Total distance to be covered = (360 + 140) m = 500 m.

Let the length of the train be x metres and its speed by y m/sec.

∴ 9y - 5 = x and 10(9y - 10) = 9x

⟹ 9y - x = 5 and 90y - 9x = 100.

On solving, we get: x = 50.

∴ Length of the train is 50 m.

∴   x = 3, as 632 is divisible 8.

So, the required number must be divisible by each one of 3, 7, 47

553681 → (Sum of digits = 28, not divisible by 3)

555181 → (Sum of digits = 25, not divisible by 3)

555681 is divisible by 3, 7, 47.

On dividing 2497 by 60, the remainder is 37.

∴ Number to be added = (60 - 37) = 23.

Then, (17)^{3.5 + x} = 17⁸.

∴ 3.5 + x = 8

⟹ x = (8 - 3.5)

⟹ x = 4.5

A leap year has (52 week + 2 days).
So, the number of odd days in a leap year is 2

Series pattern
16 x 0.25 = 4,
4 x 0.50 = 2,
2 x 0.75 =1.5,
1.5 x 1.00 = 1.5
Should come in place of 1.75
1.5 x 1.25 = 1.875
Clearly, 1.75 is wrong and will be replaced by 1.5

The ratio of speeds = The ratio of distances, when time is constant
? The ratio of distance covered by leopard to the tiger = 12 : 25
Again, ratio of rounds made by leopard to the tiger = 12 : 25
hence, leopard makes 48 rounds, when tiger makes 100 rounds