Question

A 280 ml mix real juice pack contain mixture of mango juice and orange juice in the ratio of 9:5 . if x ml juice taken out from pack & 20 ml of orange juice mixed in pack so the new ratio of mango juice & orange juice become 7:5 , then find what quantity of mango juice taken out from pack initially ?

Answer 1

$\huge\mathfrak\blue{Answer:-}$

Given:

A 280 ml mix real juice pack contain mixture of mango juice and orange juice in the ratio of 9:5 . if x ml juice taken out from pack & 20 ml of orange juice mixed in pack so the new ratio of mango juice & orange juice become 7:5.

To Find:

What quantity of mango juice taken out from pack initially.

Solution:

Given total quantity of juice = 280ml

The ratio of mango to orange juice parts is 9 : 5.

Thus, mango juice volume

= [9/(9+5)]×Total volume

= [9/14 × 280] ml

= 180 ml

Orange juice volume

= [5/14 × 280] ml

= 100 ml

Next, y ml of mango juice is taken out.

So, mango juice remaining = (180-y) ml

And, 20 ml orange juice is added.

So, orange juice now

= (100+20)ml

= 120ml

So, mango to orange juice ratio now is

= (180-y)/120

Given, this ratio = 7:5.

So, (180-y)/120 = 7/5

⇒840 = 900 - 5y

⇒ 5y = 60

⇒ y = 60/5

= 12 ml

So, 12ml of mango juice was removed earlier.

Answer 2

Answer:

$\implies$ y = 12ml.

$\large\underline\mathrm{Given:-}$

• A 280 ml mix real juice pack contain mixture of mango juice and orange juice in the ratio of 9:5 . if x ml juice taken out from pack & 20 ml of orange juice mixed in pack so the new ratio of mango juice & orange juice become 7:5

$\large\underline\mathrm{To \: find}$

• The quantity of mango juice taken out from Puch initially.

$\large\underline\mathrm{Solution}$

• Let the total quantity of juice = 280ml.
• The ratio of mango to orange juice part is 9:5.

Thus, volume of mango juice.

$\implies$ 9/(9+5) × 280

$\implies$ 9/14 × 280

$\implies$ 180ml.

$\implies$ Volume of orange juice

$\implies$ 5/14 × 280ml

$\implies$ 100ml.

y, ml of mango juice is taken out.

so, mango juice remaining = (180 - y)ml.

and, 20ml orange juice is added so, orange juice.

$\implies$ (100 + 20)ml.

$\implies$ 120ml.

So, mango to orange juice ratio now.

$\implies$ (180 - y)/120

Given the ratio = 7:5

so,

$\implies$ (180 - y)/120 = 7/5

$\implies$ 840 = 900 - 5y

$\implies$ 5y = 900 - 840

$\implies$ 5y = 60

$\implies$ y = 60/5

$\implies$ y = 12ml.

Hence, 12ml of mango juice was removed.