Practice Questions
Concept Explanation
Algebra word problems translate a real situation into equations. Identify the unknown, write relationships, and solve.
Strategy
- Define the variable clearly (what you are finding).
- Convert phrases: "is" means =, "more than" means +, "less than" means −.
- Check the answer in the original context.
Example
Tickets cost Rs. 50 each. Total paid Rs. 350. Number bought: 50x = 350, x = 7.
Common Trap
"A is 5 less than B" means A = B − 5, not B = A − 5.
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Q1 Easy
Each pen at a stationery shop costs Rs. 15. A student has Rs. 90 to spend on pens only. How many pens can the student buy?
Explanation90 ÷ 15 = 6. -
Q2 Easy
When a certain number is increased by 8, the result is 35. What is the original number?
Explanationx + 8 = 35, x = 27. -
Q3 Easy
The length of a rectangular plot is 5 cm more than its width. If the width measures 8 cm, what is the length of the plot?
Explanation8 + 5 = 13 cm. -
Q4 Easy
A train covers a distance of 240 km in 4 hours at a uniform speed. What is the speed of the train in km/h?
Explanation240 ÷ 4 = 60 km/h. -
Q5 Easy
A shopkeeper sold several items at Rs. 20 each and received a total of Rs. 300. How many items did the shopkeeper sell?
Explanation20x = 300, x = 15. -
Q6 Medium
Twice a certain number decreased by 7 equals 23. What is that number?
Explanation2x − 7 = 23, 2x = 30, x = 15. -
Q7 Medium
The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:
Explanation10 chairs = 4 tables gives chair Rs. 200, table Rs. 500. So 12 chairs + 3 tables = Rs. 3900.
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Q8 Easy
The perimeter of a square field is 48 cm. What is the length of one side of the field?
Explanation4s = 48, s = 12. -
Q9 Easy
A daily-wage worker earns Rs. 250 per day. How many days must the worker work to earn Rs. 3000 in total?
Explanation3000 ÷ 250 = 12. -
Q10 Medium
Three numbers are in the ratio 2 : 3 : 4, and their total sum is 90. What is the largest of the three numbers?
Explanation9k = 90, k = 10. Largest = 40. -
Q11 Hard
A person has only Rs. 1 and Rs. 2 coins with her. If the total number of coins that she has is 30 and the amount of money with her is Rs. 45, then the number of Rs. 2 coins is:
Explanationx + y = 30, x + 2y = 45 gives y = 15. -
Q12 Medium
Person A is 6 years older than person B, and the sum of their present ages is 46 years. How old is A now?
ExplanationA = 26, B = 20. -
Q13 Medium
A car consumes 5 litres of fuel for every 100 km driven. How many litres of fuel are needed for a journey of 360 km?
Explanation5/100 × 360 = 18 litres. -
Q14 Hard
If 4 men can complete a piece of work in 12 days, how many days will 6 men take to finish the same work, assuming each man works at the same rate?
ExplanationTotal work = 48 man-days. 48/6 = 8 days.
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DS1 Easy
A student buys pens at Rs. 15 each and spends Rs. 90 in total. How many pens were purchased?
Statement IEach pen costs Rs. 15.
Statement IITotal spent is Rs. 90.
ExplanationNeed both: 90/15 = 6 pens. -
DS2 Easy
The length of a rectangle is 5 cm more than its width. If the length is 13 cm, what is the width of the rectangle?
Statement ILength is 13 cm.
Statement IILength exceeds width by 5 cm.
ExplanationNeed both: width = 8 cm.
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DS3 Medium
A sum of Rs. 500 is divided between A and B so that A receives Rs. 120 more than B. What is B's share?
Statement ITotal is Rs. 500.
Statement IIA gets Rs. 120 more than B.
ExplanationNeed both: B = 190. -
DS4 Hard
A purse contains only Rs. 1 and Rs. 2 coins, with 30 coins in total worth Rs. 45. How many Rs. 2 coins are in the purse?
Statement IThere are 30 coins total.
Statement IITotal value is Rs. 45.
ExplanationNeed both equations to get 15 Rs. 2 coins.