Question

The Grand Old Duke of York had 10 000 men. He lost 10% of them on way to the top of

the hill, and he lost 15% of the rest as he marched them back down the hill.
What percentage of the 10 000 men were still there when they reached the bottom of
the hill?

Answer 1

76.5%

Explanation:

He lost 10% of them on way to the top of the hill

10% of 10,000 men

= 0.1 * 10,000

= 1,000 men

Remaining men = 10,000 - 1,000

= 9,000 men

15% of the rest as he marched them back down the hill.

15% of 9,000 men

= 0.15 × 9000

= 1,350 men

Total men remaining = 9000 - 1,350

= 7,650 men

% remaining =

x% of 10000 men = 7,650

x/100 * 10,000 = 7,650

Cross product

10,000x =7,650 * 100

10,000x = 765,000

x = 765,000/10,000

= 76.5%

x = 76.5%