Shortcut Trick
WaterAcid = [2×(97)]+[5×(95)][2×(92)]+[5×(94)]
WaterAcid = 914+92594+920
WaterAcid = 24/39 = 8 :13
∴ The correct answer is 8 : 13.
GIVEN:
In 1st container, acid : water = 2 ∶ 7
In 2nd container, acid : water = 4 ∶ 5
Ratio of mixture = 2 ∶ 5
CALCULATION:
Let "x" be the acid content of the New mixture
Using the principal of allegation
⇒ [(4/9) - x]/[x - (2/9)] = 2/5
⇒ 4/9 - x = 2x/5 - 4/45
⇒ 7x/5 = 4/9 + 4/45
⇒ 7x/5 = 24/45
⇒ x = 8/21
Ratio of Acid : water in the new mixture = 8 : (21 - 8)
Ratio of Acid : water in the new mixture = 8 ∶ 13
∴ The required ratio is 8 ∶ 13.
Alternate MethodGiven,
Ratio of mixture in container 1 = 2 : 7 (sum = 9)
Ratio of mixture in container 2 = 4 : 5 (sum = 9)
Let they contains 90L mixture in both container initially.
Acid in container 1 = 90 × 2/9 = 20L
Similarly,
Water in container 1 = 90 × 7/9 = 70L
Acid in container 2 = 90 × 4/9 = 40L
Water in container 2 = 90 × 5/9 = 90L
Now, we have to mix it in the ratio of 2 : 5 mean
Means 20% from Container 1 & 50 % of Container 2
So,
Acid from Container 1 = 20% of 20L = 4L
Acid from Container 2 = 50% of 40L = 20L
Total Acid in final Mixture = 4 + 20 = 24 L
Water from Container 1 = 20% of 70L = 14L
Acid from Container 2 = 50% of 50L = 25L
Total Acid in final Mixture = 14 + 25 = 39 L
So required ration = 24/39 = 8/13 = 8 :13