A smoothie contains fruit extracts and yogurt in the ratio 5:1 .On adding 5 litres of yogurt the ratio of fruit extract to yogurt becomes 5:2 .what is the quantity of fruit extract in the smoothie?
Answers
Step-by-step explanation:
Given :-
A smoothie contains fruit extracts and yogurt in the ratio 5:1 .On adding 5 litres of yogurt the ratio of fruit extract to yogurt becomes 5:2 .
To find :-
What is the quantity of fruit extract in the smoothie?
Solution :-
Given that
The ratio of fruit extracts and yogurt in the smoothie = 5:1
Let they be 5X litres and X litres
The quantity of fruit extracts = 5X litres
The quantity of yogurt = X litres
On adding 5 litres of Yogurt then it becomes
(X+5) litres
Now , The new ratio = 5X : (X+5)
According to the given problem
The new ratio of fruit extract to the yogurt = 5:2
=> 5X : (X+5) = 5:2
=> 5X / (X+5) = 5/2
On applying cross multiplication then
=> 5X×2 = 5(X+5)
=> 10X = 5X +25
=> 10X-5X = 25
=> 5X = 25
=> X = 25/5
=> X = 5
Now,
Fruit extract = 5X = 5(5) = 25 litres
Answer:-
The quantity of fruit extracts in the smoothie is
25 litres
Check :-
Quantity of fruit extracts = 25 litres
Quantity of yogurt = 5 litres
Their ratio = 25:5 = 5:1
In adding 5 litres of Yogurt to the smoothie then
The new ratio = 25: 5+5
=> 25:10
=> 5:2
Verified the given relations in the given problem.
Answer:
25 litres
Step-by-step explanation:
Let the quantity of fruit extract be x litres
and that of yogurt be y litres
so initially,
x/y = 5
⇒ x = 5y
after adding 5 litres yogurt,
x/(y+5) = 5/2
Solving both equations by substituting,
5y/(y+5) = 5/2
⇒ 10y = 5y + 25
⇒ y = 5
∵ x = 5y
∴ x = 25