5. There are two containers A
and B, each filled with NaCl and
water in the ratio 3:5 and 5:7
respectively. A new mixture is
formed by mixing the contents
of A and B in the ratio 1:2. What
is the ratio of composition of
NaCl and water in the new
mixture?
26:43
29:43
9:3
26:29
Answers
Given : two containers A and B, each filled with NaCl and water in the ratio 3:5 and 5:7 respectively . A new mixture is formed by mixing the contents of A and B in the ratio 1:2
To find : ratio of composition of NaCl and water in the new mixture
Solution:
containers A - NaCl = 3A & Water = 5A Total = 8A
containers B - NaCl = 5B & Water = 7B Total = 8B
Let Say Mixture from A = k
Then mixture from B = 2k
NaCl = (3A/8A)k + (5B/12B)2k = 3k/8 + 5k/6
= (9k + 10k)/24
= 29k/24
Water = (5A/8A)k + (7B/12B)2k = 5k/8 + 7k/6
= (15k + 28k)/24
= 43k/24
ratio of composition of NaCl and water in the new mixture
= 29k/24 : 43k/24
= 29 : 43
ratio of composition of NaCl and water in the new mixture = 29 : 43
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✰✰|| Given ||✰✰
- Ratio of mixture of NaCI & water in container A = 3 : 5
- Ratio of mixture of NaCI & water in container B = 5 : 7
✰✰|| To Find ||✰✰
- ratio of composition of NaCl and water in new mixture
✪|| Solution ||✪
NaCI from container A = 3/8 × 1/3
⇒ NaCI from container A = 1/8
NaCI from container B = 5/12 × 2/3
⇒ NaCI from container B = 10/36
Water from container A = 5/8 × 1/3
⇒ Water from container A = 5/24
Water from container B = 7/12 × 2/3
⇒Water from container B = 14/36
Ratio of NaCl & water in new mixture = total quantity of NaCI : Total quantity of water
⇒ Ratio of NaCl & water in new mixture = 1/8 + 10/36 : 5/24 + 14/36
⇒ Ratio of NaCl & water in new mixture = 9 + 20/72 : 15 + 28/72
⇒ Ratio of NaCl & water in new mixture = 29/72 : 43/72
⇒ Ratio of NaCl & water in new mixture = 29 : 43