Top 10 Numerical Ability Speed Hacks: Work Problems, Ratios & Percentages

1. Work Problems: The Product-Over-Sum Formula

Standard Problem:

*Worker A finishes a painting job in 10 hours. Worker B finishes the same job in 15 hours. How long will it take them to finish the job together?*

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Fast Method:

$$\text{Combined Time} = \frac{A \times B}{A + B} = \frac{10 \times 15}{10 + 15} = \frac{150}{25} = 6 \text{ hours}$$

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2. Percentage Mental Trick: 10% + 5% Decomposition

#### Problem:

*Find 15% of 480.*

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Step-by-Step Mental Calculation:

1. **Find 10%:** Move the decimal point one digit to the left $\rightarrow 48.0$.2. **Find 5%:** Divide 10% in half $\rightarrow 48 / 2 = 24.0$. 3. **Add 10% + 5%:** $48 + 24 = 72$.

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3. Ratio Distribution: The Total-Parts Formula

Problem:

*A profit of ₱45,000 is to be shared among three partners in the ratio 2 : 3 : 4. How much is the largest share?*

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Fast Method:

1. **Sum the ratio parts:** $2 + 3 + 4 = 9 \text{ parts}$.2. **Find the value per part:** $\text{Value per part} = ₱45,000 / 9 = ₱5,000$. 3. **Calculate largest share (4 parts):** $4 \times ₱5,000 = ₱20,000$.