Pariksha SaathiSimple Equations Questions with Solutions
The hard part of these questions isn’t solving the equation — it’s translating the sentence into one. Once the word problem becomes algebra, it’s routine. Here’s the approach, four fully worked examples, and a few to try yourself.
The approach, quickly
- Assign a variable to the unknown quantity the question actually asks for, and translate each sentence into an equation using that variable (and a second variable if there are two unknowns).
- Phrases translate directly: "sum of" → +, "difference of" → −, "X more than Y" → Y + X, "X less than Y" → Y − X, "twice/three times a number" → 2x/3x.
- With two unknowns, you need two independent equations — write both before trying to solve either one.
- Once solved, substitute your answer back into BOTH original sentences (not just the equation) to confirm it actually satisfies the word problem, not just the algebra.
Worked examples
1. The sum of two numbers is 45, and their difference is 11. Find the two numbers.
Solution
- Let the numbers be x and y: x + y = 45 and x − y = 11.
- Adding the two equations: 2x = 56, so x = 28.
- Substituting back: y = 45 − 28 = 17.
Answer: 28 and 17
2. Five years ago, a father was three times as old as his son. Ten years from now, the father will be twice as old as the son. Find their present ages.
Solution
- Let the son’s present age = s and the father’s present age = f.
- Five years ago: f − 5 = 3(s − 5), so f = 3s − 10.
- Ten years from now: f + 10 = 2(s + 10), so f = 2s + 10.
- Setting these equal: 3s − 10 = 2s + 10, so s = 20, and f = 2(20) + 10 = 50.
Answer: Father: 50 years, Son: 20 years
3. A number is 8 more than twice another number. If the sum of the two numbers is 50, find both numbers.
Solution
- Let the numbers be x and y, with x = 2y + 8.
- Substituting into x + y = 50: (2y + 8) + y = 50, so 3y = 42, giving y = 14.
- Then x = 2(14) + 8 = 36.
Answer: 36 and 14
4. Three times a number, decreased by 7, equals twice the number increased by 9. Find the number.
Solution
- Let the number be x: 3x − 7 = 2x + 9.
- Subtracting 2x from both sides: x − 7 = 9, so x = 16.
Answer: 16
Try these yourself
Translate the sentence into an equation first, then solve, and check against the answer.
1. The sum of two numbers is 60, and their difference is 14. Find the two numbers.
Answer: 37 and 23
2. A number is 5 more than three times another number. If the sum of the two numbers is 45, find both numbers.
Answer: 35 and 10
3. Four times a number, decreased by 9, equals the number increased by 21. Find the number.
Answer: 10
Where this comes up
Simple Equations is tested directly in the Quantitative/Numerical Aptitude section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk.
Practice more Simple Equations questions
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