Question

Sarah and Henry share some sweets in the ratio 5:6 . Sarah eats 24 of her sweets and the ratio of sweets left becomes 1:2 . How many sweets did Henry have?

Answer 1

The number of sweets did Henry have is 72

Explanation:

Given as :

The ratio of Sarah to Henry share sweets = 5 : 6

So, Let The Sarah share = 5 x

And The Henry share = 6 x

Now, again Sarah eats 24 of her sweets , then new ratio becomes 1:2

∴
`(5 x - 24)/(6 x)` =
`(1)/(2)`

Or, 2 × (5 x - 24 ) = 1 × 6 x

Or, 10 x - 48 = 6 x

Or, 10 x - 6 x = 48

So, 4 x = 48

∴ x =
`(48)/(4)` = 12

So, the number of sweets did Henry have = 6 x = 6 × 12 = 72

The number of sweets did Sarah have = 5 x = 5 × 12 = 60

Hence The number of sweets did Henry have is 72 Answer