Grandmother's Punch hangover cure is a mix of two ingredients: a herba

Two main ingredients include:
1. Herbal extraction (HE) containing 20% alcohol
2. Apricot cider (AC) containing 5% alcohol

Let the total concentration of HE be x milliliters and the total concentration of AC be y milliliters.
Then, the amount of alcohol contained in HE = 20% of x = \(\frac{x}{5}\)
The amount of alcohol contained in AC = 5% of y = \(\frac{y}{20}\)

Given, the total amount of alcohol contained in the bottle = 87 milliliters
Thus, \(\frac{x}{5}\) + \(\frac{y}{20}\) = 87 ⟹ 4x + y = 1740 ………. (1)

Also, total concentration of the two ingredients = 750
Thus, x + y = 750 ………. (2)

Solving (1) and (2) simultaneously, we get
4x + y = 1740 ………. (1) × 1
x + y = 750 ………. (2) × 4

4x + y = 1740 ……… (1)
4x + 4y = 3000 ………. (3)

On subtracting (1) from (3), we get:
3y = 1260
⟹ y = 420

Hence, the correct answer is Option B.

Alligation.

% of alcohol in mixture = \(\frac{87 *100 }{750}\) = \(\frac{58}{5\\
}\\
\)


Apricot______:_______Herbal
5__________________20
__________58/5_______
20-(58/5)________(58/5)-5

Apricot : Herbal = \((20-\frac{58}{5}): (\frac{58}{5}-5)\)

\(\frac{Apricot cider }{ Total}\) = \( (20-\frac{58}{5}) / [(20-\frac{58}{5}) + (\frac{58}{5})-5]\\
\)


\(\frac{Apricot cider}{750 }\) = \(\frac{42}{5*15}\)
Apricot cider = \(\frac{(42 * 750) }{ (5 * 15)} = 420 (B)\\
\)