MKS CMAT · Quantitative Ability
Ratio, Proportion and Averages for CMAT: Methods and Practice
Ratio, proportion and averages become much easier when you separate the relationship from the actual values. A ratio tells how quantities compare, a proportion states that two ratios are equal, and an average describes a total shared equally across a number of observations.
This lesson contains original MKS examples and practice. They are not TU past-paper questions and do not predict a live examination.
YOUR LEARNING ROUTE
Build the skill. Then apply it.
Build the three ideas correctly
Ratio
The ratio 3:5 has eight equal parts. If the total is 64, one part is 64 ÷ 8 = 8, so the quantities are 24 and 40. A ratio has no fixed size until one real value or total is supplied.
Direct and inverse proportion
In direct proportion, both quantities move in the same direction at a constant rate. If four notebooks cost NPR 600, one costs NPR 150 and seven cost NPR 1,050. In inverse proportion, one quantity rises while the other falls: with equal work rates, more workers need fewer days.
Average
Average = total ÷ number of values. Work backwards when a value is missing: required total = target average × number of values. For combined groups, add the group totals; do not simply average two averages unless the group sizes are equal.
Six original questions
Q1. Dividing a total by a ratio
Two study groups have members in the ratio 3:5. Together they have 64 members. How many are in the smaller group?
- A. 16
- B. 24
- C. 32
- D. 40
Q2. Direct proportion
Four notebooks cost NPR 600 at the same unit price. What do seven notebooks cost?
- A. NPR 900
- B. NPR 1,000
- C. NPR 1,050
- D. NPR 1,200
Q3. Missing value from an average
Five practice scores have an average of 74. Four scores are 72, 68, 80 and 75. What is the fifth score?
- A. 70
- B. 72
- C. 75
- D. 78
Q4. Combined average
Twelve students have an average score of 68 and eight students have an average of 77. What is the combined average?
- A. 71.0
- B. 71.6
- C. 72.5
- D. 73.0
Q5. Inverse proportion
Six equally efficient workers complete a task in 15 days. At the same rate, how many days would ten workers need?
- A. 6
- B. 9
- C. 12
- D. 25
Q6. A changed ratio
The ratio of boys to girls in a club is 4:5. After six boys join, the ratio becomes 10:11. How many members were in the club before the change?
- A. 81
- B. 90
- C. 99
- D. 110
PAUSE · CHECK · IMPROVE
Use the next section as an action step.
Keep your working and source notes. Record what was uncertain, then choose one small correction or verification task before moving on.
Answers and explanations
Q1 — B, 24. There are 3 + 5 = 8 parts. One part is 64 ÷ 8 = 8, and the smaller group has 3 × 8 = 24 members.
Q2 — C, NPR 1,050. Unit cost = 600 ÷ 4 = 150. Seven cost 7 × 150 = 1,050. The relationship is direct because the unit price is fixed.
Q3 — C, 75. The required total is 74 × 5 = 370. The four known scores total 295, so the missing score is 370 − 295 = 75.
Q4 — B, 71.6. The first group total is 12 × 68 = 816; the second is 8 × 77 = 616. Combined average = (816 + 616) ÷ 20 = 71.6. Averaging 68 and 77 would incorrectly give the two groups equal weight.
Q5 — B, 9 days. Total work is 6 × 15 = 90 worker-days. With ten workers, time = 90 ÷ 10 = 9 days.
Q6 — C, 99. Let the original numbers be 4k and 5k. Then (4k + 6)/(5k) = 10/11. Solving gives 44k + 66 = 50k, so k = 11. Original total = 9k = 99.
Common mistakes to record
- Adding ratio numbers directly to a real total without first finding one part.
- Treating every relationship as direct proportion.
- Averaging group averages without using group sizes.
- Rounding an intermediate value before the final step.
- Forgetting that a changed ratio requires an equation.
Use the Quantitative Ability guide for the wider topic map and CMAT sample questions for mixed-section practice.
Questions and explanations are original MKS learning material. Study scenes are AI-generated illustrations.
Keep your preparation moving.
Explore the wider CMAT learning route or find current class information with MKSPrep.
