DS Percent Question

[Strongt]

By what percent did the price of a book increase?

1- The ratio of the book's original price to its new price is 4:5
2- The ratio of the chnage in the book's price to its new price is 1:5

Answer is d

I got it right but I want to know if there is a systemitic way to answer these type of questions

[shankar.ashwin]

Most problems in percentages can be verified by using numbers.
Here,

Let the original cost of book = 100 and New cost be = x

(1) says Org/New = 100/x = 4/5 (or) x=125. Thats a 25% increase. (sufficient)

(2) says (New-Org)/New = (x-100)/x = 1/5. Again you have x=125 (or) a 25% increase. (sufficient)

You don't actually have to find the percent increase, but from each statement you could see theres one unknown 'x' and a equation, so it can be found.

[neelgandham]

You will be able to find out the % increase if you know at least two of the variables among Increase,Original price, New price or if you know at least two of the ratios Increase/Original price, Increase/New price, Original price/New price

From 1)We know the ratio Original price/New price - Sufficient !
From 2)We know the ratio Increase/New price - Sufficient!

Hence D