Question

In a juice corner a juice maker mixes 48 litre of Orange juice with 144 litre of Pineapple juice in a vessel.
litre of total mixture is taken out and 32 litre Orange Juice and 48 litre Pineapple juice are added in the
mixture. The final mixture contains 30% Orange juice, find the quantity of the mixture that is taken out.

Answer 1

Answer:

Ans: 32 Litres

Step-by-step explanation:

Given:

orange juice=48 litre

pineapple juice=144 litre

total quantity of juice = (48+144) = 192 litres

added orange juice =32 litres

added pineapple juice=48 litres

final mixture = 30% of Orange juice

To find : X

Soln:

X litre mixture has the same ratio quantity of the orange juice and pineapple juice as in the earlier mixture( i.e. 48/144 ) .

Amount of orange juice taken out (48/(48+144) = 48/192 = 1/4) = X/4.

[amount of juice removed = (quantity of juice/total mixture)*mixture taken out]

orange juice left in the mixture=(48-(X/4)+32)=80-(X/4)

total mixture=48+144+32+48-X = 272-X

%of orange juice = 30% = (80-(X/4))/(272-X)

30/100 = (320-X)/(1088-4X)

solving this

X=32

May this help you all...

Answer 2

• The quantity of the mixture that is taken out is equal to 32 litre .

Given :-

• Orange juice mixed = 48 litre .
• Pineapple juice mixed = 144 litre .
• Mixture taken out = x litre .
• Orange juice added = 32 litre .
• Pineapple juice added = 48 litre .
• Final mixture contains = 30% orange juice .

To Find :- Value of x ?

Solution :-

→ Orange juice mixed : Pineapple juice mixed = 48 : 144 = 1 : 3

So, In x litre of mixture which is taken out ,

→ Orange juice taken out = (1/4) of x = (x/4) litre

→ Pineapple juice taken out = (3/4) of x = (3x/4) litre

then,

→ Orange juice left in the mixture = {48 - (x/4)} litre

→ Pineapple juice left in the mixture = {144 - (3x/4)} litre

now,

→ Orange juice added in mixture = 32 litre

→ Total orange juice in final mixture = {48 - (x/4)} + 32 = 48 + 32 - (x/4) = 80 - (x/4) = {(320 - x)/4} litre ----- Equation (1)

and,

→ Pineapple juice added in mixture = 48 litre

→ Total Pineapple juice in final mixture = {144 - (3x/4)} + 48 = 144 + 48 - (3x/4) = 192 - (3x/4) = {(768 - 3x)/4} litre ------- Equation (2)

therefore,

→ Final mixture = Equation (1) + Equation (2)

→ Final mixture = {(320 - x)/4} + {(768 - 3x)/4}

→ Final mixture = (320 - x + 768 - 3x)/4

→ Final mixture = (1088 - 4x)/4

→ Final mixture = 4(272 - x)/4

→ Final mixture = (272 - x) litre -------- Equation (3)

A/q,

→ Orange juice in final mixture = 30% of final mixture

→ Equation (1) = 30% of Equation (3)

→ {(320 - x)/4} = (30/100) × (272 - x)

→ {(320 - x)/4} = 3(272 - x)/10

→ (320 - x)/4 = (816 - 3x)/10

→ (320 - x)/2 = (816 - 3x)/5

cross - multiply,

→ 5(320 - x) = 2(816 - 3x)

→ 1600 - 5x = 1632 - 6x

→ 6x - 5x = 1632 - 1600

→ x = 32 litre (Ans.)

Hence, Value of x is equal to 32 litre .

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