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:The number of sweets did Henry have is 72Step-by-step 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 xNow, again Sarah eats 24 of her sweets , then new ratio becomes 1:2∴ [tex]\frac{5 x - 24}{6 x}[/tex] = [tex]\frac{1}{2}[/tex] Or, 2 × (5 x - 24 ) = 1 × 6 xOr, 10 x - 48 = 6 x Or, 10 x - 6 x = 48 So, 4 x = 48 ∴       x = [tex]\frac{48}{4}[/tex] = 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