Ratio and proportion

Ratio and proportion is a Aptitude concept from the MPSC syllabus, tested in 15 past MPSC questions across 8 exam years between 2014 and 2025. Below are those real questions with their correct answers and explanations, plus the concepts worth being comfortable with first.

Real questions

Years tested

8 · 2014–2025

In context

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Asked in

2025 2024 2023 2021 2020 2018 2017 2014

What you need to know first

Linear equationsRatio basicsBasic algebraFractionsRatio ConceptsCircle CircumferenceBasic ProportionsBasic RatiosPercentage/Multiplying FactorsSolving linear equationsSimple equationsLogical ReasoningFractional reductionBasic ratio conceptsBasic division and multiplicationBasic algebraic equationsConcept of ratiosBasic arithmeticRatio simplificationLinear equations in one variable

What mastering this unlocks

Data InterpretationLine GraphsCustom clock parametersRelative speed of clock handsData Sufficiency Speed, Time and Distance Percentage Successive Percentage Chain Rule Time and Work Escalator Problems Relative speed

Real questions that test this

सविता आणि कविता यांच्या आजच्या वया चे गुणोत्तर 3 : 4 आहे. 5 वर्षांनंतर त्यांच्या वयाचे गुणोत्तर 4 : 5 होईल, तर सविता आणि कविता यांची आजची वये काढा. The present ages of Savita and Kavita are in the ratio 3 : 4. After five years the ratio of their ages will be 4 : 5. Find the present ages of Savita and Kavita.

1)सविता 20 वर्षे आणि कविता 15 वर्षे / Savita 20 years and Kavita 15 years

2)सविता 15 वर्षे आणि कविता 20 वर्षे / Savita 15 years and Kavita 20 years✓ Correct

3)सविता 20 वर्षे आणि कविता 25 वर्षे / Savita 20 years and Kavita 25 years

4)सविता 25 वर्षे आणि कविता 20 वर्षे / Savita 25 years and Kavita 20 years

Let present ages be 3x and 4x. After 5 years, (3x+5)/(4x+5) = 4/5, solving gives x=5, so ages are 15 and 20 years.

प्रश्नचिन्हाच्या जागी अचूक पर्याय निवडा. जर p/q = 5/4, तर (3p + 2q)/(3p - 2q) = ? Replace the question mark choosing the correct alternative. If p/q = 5/4, then (3p + 2q)/(3p - 2q) = ?

1)32/7

2)15/8

3)23/7✓ Correct

4)8/15

Substitute p = 5x and q = 4x into the expression (3(5) + 2(4)) / (3(5) - 2(4)) which evaluates to (15+8)/(15-8) = 23/7.

‘दहा विद्यार्थी परीक्षा अनुत्तीर्ण झाले' हा निष्कर्ष नेहमी सत्य ठरवणारी दोन तथ्ये ओळखा. तथ्ये : a. 40 विद्यार्थी परीक्षा उत्तीर्ण झाले. b. 10 विद्यार्थीने परीक्षा पूर्ण केली नाही म्हणून ते उत्तीर्ण वा अनुत्तीर्ण झाले नाहीत. c. अनुत्तीर्ण झालेल्या विद्यार्थ्यांची संख्या परीक्षा पूर्ण न करणाऱ्यांपेक्षा 5 : 1 ने जास्त आहे. d. उत्तीर्ण झालेल्या विद्यार्थ्यांची संख्या अनुत्तीर्ण विद्यार्थ्यांपेक्षा 4 : 1 ने जास्त आहे. Identify two facts that prove conclusion : 'Ten students failed the exam' to be always true. Facts : a. 40 students passed the exam. b. 10 students did not complete the exam and so neither passed nor failed. c. Number of students who failed outnumbered those who did not complete exam by 5 : 1. d. Number of students who passed outnumbered those who failed by 4 : 1.

(a)40 विद्यार्थी परीक्षा उत्तीर्ण झाले. / 40 students passed the exam.

(b)10 विद्यार्थीने परीक्षा पूर्ण केली नाही म्हणून ते उत्तीर्ण वा अनुत्तीर्ण झाले नाहीत. / 10 students did not complete the exam and so neither passed nor failed.

(c)अनुत्तीर्ण झालेल्या विद्यार्थ्यांची संख्या परीक्षा पूर्ण न करणाऱ्यांपेक्षा 5 : 1 ने जास्त आहे. / Number of students who failed outnumbered those who did not complete exam by 5 : 1.

(d)उत्तीर्ण झालेल्या विद्यार्थ्यांची संख्या अनुत्तीर्ण विद्यार्थ्यांपेक्षा 4 : 1 ने जास्त आहे. / Number of students who passed outnumbered those who failed by 4 : 1.

1)a, b

2)b, c

3)a, d✓ Correct

4)b, d

Fact (a) gives 40 students passed, and fact (d) says those who passed outnumber those who failed by 4 : 1. So failed = 40 / 4 = 10, always. Facts (b) and (c) only tell us 10 did not complete and a ratio involving them, which never fixes the number who failed on its own with (b) or (d).

ट्रॅक्टरच्या मोठ्या व लहान चाकाचा व्यास अनुक्रमे 50 से.मी. व 35 से.मी. आहे. जेव्हा मोठ्या चाकाचे 21 फेरे पूर्ण होतील तेव्हा लहान चाकाचे किती फेरे पूर्ण होतील? The diameters of the bigger wheel and smaller wheel of a tractor are 50 cm and 35 cm respectively. How many revolutions will the smaller wheel make when the bigger one makes 21 revolutions ?

1)25

2)45

3)30✓ Correct

4)32

The distance covered by a wheel in one revolution is its circumference (π × diameter). Equate the total distance covered by both wheels: 50 × 21 = 35 × x, which gives x = 30.

अमनने रु. 70,000 गुंतवून एक उद्योग सुरू केला. राखी या उद्योगामध्ये सहा महिन्यांनंतर आली व त्यावेळी तिने रु. 1,05,000 गुंतविले. सागरने पुढील सहा महिन्यांनंतर याच उद्योगामध्ये रु. 1.4 लाख गुंतविले व उद्योगामध्ये आला. जर तीन वर्षांनंतर या उद्योगामधील नफा अमन, राखी व सागर यांच्यामध्ये वाटावयाचा असेल तर तो कोणत्या प्रमाणात वाटावा ? Aman started a business investing Rs. 70,000, Rakhi joined him after six months with an amount of Rs.1,05,000 and Sagar joined them with Rs.1.4 lakh after next six months. What should be the ratio of the amount of profit earned which should be distributed among Aman, Rakhi and Sagar after three years ?

a)7 : 6 : 10

b)12 : 15 : 16✓ Correct

c)42 : 45 : 36

d)42 : 50 : 48

Profit ratio is calculated by multiplying the invested capital by the time period for which it is invested: Aman (70000 * 36), Rakhi (105000 * 30), Sagar (140000 * 24). Simplifying this gives 12 : 15 : 16.

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