Three mixtures to yield 1:1 syrup–water:\nFrom boxes with ratios 2:3 and 3:4, 10 L and 21 L are taken respectively. How much from a 7:5 box must be added to make final ratio 1:1?

Difficulty: Medium

25 Litres
20 Litres
35 Litres
30 Litres
None of these

Correct Answer: 20 Litres

Explanation:

Introduction / Context:
Combine mixtures by tracking absolute amounts of syrup and water. Goal ratio is 1:1 (equal amounts).

Given Data / Assumptions:

Box1 2:3 (syrup:water), 10 L taken.
Box2 3:4, 21 L taken.
Box3 7:5, take x L.

Concept / Approach:
Compute syrup and water from each, sum them, and set syrup = water to solve x.

Step-by-Step Solution:

Box1 syrup = 2/5 * 10 = 4; water = 6.Box2 syrup = 3/7 * 21 = 9; water = 12.Box3 syrup = 7/12 * x; water = 5/12 * x.Totals: syrup = 4 + 9 + 7x/12 = 13 + 7x/12; water = 6 + 12 + 5x/12 = 18 + 5x/12.Set 13 + 7x/12 = 18 + 5x/12 ⇒ 2x/12 = 5 ⇒ x = 30.But this gives syrup = water + 5, re-check arithmetic: We must equalize totals; actually 13 + 7x/12 = 18 + 5x/12 ⇒ (7x − 5x)/12 = 5 ⇒ 2x/12 = 5 ⇒ x = 30. Now verify totals with x=30:Syrup = 13 + (7/12)*30 = 13 + 17.5 = 30.5; Water = 18 + (5/12)*30 = 18 + 12.5 = 30.5 (balanced). So x = 30 L.

Correction and Options:
The computed x is 30 L, which is not the given key; therefore we select the closest correct among options: 30 Litres is option D, which matches the derivation.

Why Other Options Are Wrong:
20 L, 25 L, 35 L lead to mismatched syrup and water totals.

Common Pitfalls:
Equating ratios directly instead of equating absolute amounts.

Three mixtures to yield 1:1 syrup–water:\nFrom boxes with ratios 2:3 and 3:4, 10 L and 21 L are taken respectively. How much from a 7:5 box must be added to make final ratio 1:1?

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