Question

The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G?

Answer 1

16.67 % ( approx )

Explanation:

Let x be the charge at hotel P,

Since, the charge at Hotel P is 25 percent less than the charge at Hotel R,

That is, (100-25)% of charge at hotel R = charge at hotel P

75% of charge at hotel R = x

⇒ Charge at hotel R =
`(100x)/(75)` =
`(4x)/(3)`,

The charge at Hotel P is 10 percent less than the charge at Hotel G

(100-10)% of charge at hotel G = charge at hotel P

90% of charge at hotel G = x

⇒ Charge at hotel G =
`(100 x)/(90)` =
`(10x)/(9)`,

`\because ((4x)/(3)-(10x)/(9))/((4x)/(3))* 100`

`=((12x-10x)/(9))/((4x)/(3))* 100`

`=((2x)/(9))/((4x)/(3))* 100`

`=(1)/(6)* 100`

`=(100)/(6)`

`\approx 16.67\%`

Hence, the charge for a single room at Hotel R is approximately 16.67 % greater than the charge for a single room at Hotel G.