Free Guide: Ratio Questions in Psychotechnic and Dapar Tests

How to solve ratio distribution, proportion, and ratio change questions using the "parts" method

Written by Eli Isaak • Phone: 054-5664932 • Ask me on WhatsApp

About Ratio Questions

Ratio questions appear in the quantitative section of psychotechnic and Dapar tests in many forms: splitting money among partners, mixing materials, maps and charts, as well as word problems about boys and girls, ages, and prices. The formulas are simple, but the difficulty lies in the wording: many examinees get confused regarding the order of factors, between "ratio" and "difference", and between ratio parts and the actual quantities.

The key to success is to think in terms of "parts": every ratio is a number of equal parts, and what matters is finding the value of a single part. Once you have it, everything else is multiplication and addition. Below are the two basic methods, with two solved examples for each.

The Golden Triangle of Ratio Questions:

Value of One Part = Total Quantity / Sum of Ratio Parts
Order matters: In the ratio a : b, the number a belongs to the quantity mentioned first. Therefore, the first quantity is a × (value of one part) and the second is b × (value of one part).
1
Writing and Reducing Ratios (Ratio as a Fraction)
A ratio between two quantities is written as a : b and read as "a to b". Order matters: the first number belongs to the quantity mentioned first in the question. Like a fraction, a ratio can be simplified by dividing both sides by the same number. When quantities are given in different units, convert them to the same unit first.
Example A: Ratio Between Two Numbers
A classroom has 24 boys and 36 girls. What is the ratio of boys to girls in simplified form?
  • Write the ratio: 24 : 36
  • Divide both sides by 12 (the greatest common divisor): 24 / 12 = 2 and 36 / 12 = 3
Answer: 2 : 3
Example B: Ratio Between Different Units
What is the ratio of 45 minutes to an hour and a half?
  • Convert to a single unit: an hour and a half is 90 minutes
  • Write the ratio: 45 : 90
  • Divide by 45: 45 / 45 = 1 and 90 / 45 = 2
Answer: 1 : 2
2
Dividing a Quantity by Ratio (The "Parts" Method)
To divide a quantity according to a given ratio: add the ratio parts, divide the total quantity by this sum to get the value of "one part", and multiply by each factor's part. Finally, check that the sum of the results equals the original quantity.
Example A: Two Factors
Siblings share 120 NIS in a ratio of 3 : 5. How much money does each receive?
  • Number of parts: 3 + 5 = 8
  • Value of one part: 120 / 8 = 15 NIS
  • First sibling: 3 × 15 = 45, Second sibling: 5 × 15 = 75
  • Check: 45 + 75 = 120
Answer: 45 NIS and 75 NIS
Example B: Three Factors
Three partners divide a profit of 200,000 NIS in a ratio of 2 : 3 : 5. How much does the third partner receive?
  • Number of parts: 2 + 3 + 5 = 10
  • Value of one part: 200,000 / 10 = 20,000
  • Third partner: 5 × 20,000 = 100,000
  • Check: 40,000 + 60,000 + 100,000 = 200,000
Answer: 100,000 NIS

Want to Master Many Types of Ratio Questions and Practice Dozens of Exercises?

The two methods presented here are only the beginning! The full study kit includes the most advanced tricks and models for difficult Dapar questions:

Special offer: only 230 NIS!

Contact on WhatsApp to Purchase the Full Kit →

Interested in One-on-One Personal Preparation?

Want to practice ratio questions or entire test chapters with me? In a private Zoom lesson, we will build a customized solution strategy to get you to your target score.

Schedule a Private Lesson on WhatsApp Call me: 054-5664932