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

Answer:

Sahara India in 5 : 6 ratio

Step-by-step explanation:

let the number be x

X - 24 is equal to 5

x = 29

let no be y

y- 29 =6-24

total sweet Left for Henry is 47

Answer 2

Let Sarah have "M" number of sweets and Henry have "N" number of sweets.

• Sarah and Henry share some sweets in the ratio 5:6.

According to question,

$\Rightarrow\:\dfrac{M}{N}\:=\:\dfrac{5}{6}$ ______ (eq 1)

$\Rightarrow\:M\:=\:\dfrac{5N}{6}$ _____ (eq 2)

• Sarah eats 24 of her sweets and the ratio of sweets left becomes 1:2.

According to question,

$\Rightarrow\:\dfrac{M\:-\:16}{N}\:=\:\dfrac{1}{2}$

Cross multiply them

$\Rightarrow\:2(M\:-\:16)\:=\:1(N)$

$\Rightarrow\:2M\:-\:30\:=\:N$

$\Rightarrow\:2 \bigg(\dfrac{5M}{6} \bigg)\:-\:30\:=\:N$

$\Rightarrow\:\dfrac{5M}{3}\:-\:30\:=\:N$

$\Rightarrow\:\dfrac{5M\:-\:90}{3}\:=\:N$

$\Rightarrow\:5M\:-\:90\:=\:3N$

$\Rightarrow\:5M\:-\:3M\:=\:90$

$\Rightarrow\:2M\:=\:90$

$\Rightarrow\:M\:=\:45$

Put value of M in (eq 2)

$\Rightarrow\:45\:=\:\dfrac{5N}{6}$

Cross multiply them

$\Rightarrow\:45(6)\:=\:5N$

$\Rightarrow\:270\:=\:5N$

$\Rightarrow\:N\:=\:54$

Henry have 54 sweets.

☆ Verification :

From above calculations we have M = 45 and N = 54

Put value of M and N in (eq 1)

$\Rightarrow\:\dfrac{45}{54}\:=\:\dfrac{5}{6}$

$\Rightarrow\:\dfrac{5}{6}\:=\:\dfrac{5}{6}$