ARCH-M1-05: Two-Component Mixing, Dilution Alligation & Combined Work Rates

Full 15-Q Timed Drill

Step 1 of 6 • The Core Idea

ARCH-M1-05: Why the 150s Classroom Method Fails Under the 90s Clock

Standard Classroom Method (Too Slow)~150s (Blows 90s Clock)

Scale

P : Q = 5 : 3

2

so that the middle term

Q

equals

6

, giving

P : Q = 10 : 6

. Combining with

Q : R = 6 : 7

gives

P : Q : R = 10 : 6 : 7

, so

P : R = 10 : 7

(~90s).

The Fast ShortcutTarget: 45s (Saves 105s)

Line 1 (Fraction Product):

\frac{P}{R} = \frac{P}{Q} \times \frac{Q}{R} = \frac{5}{3} \times \frac{6}{7}

.
**Line 2 (Cancel

3

):**

\frac{10}{7} \implies 10 : 7

(20s).

Where Students Lose Time: In 8 past UAT-UK questions (3.56% of Mathematics 1), candidates lose 105s by forgetting that adding solute or solvent changes the total denominator of the mixture. Instead, apply M3 with Maths 1 skill M3.5.

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