Free Logical Problems MCQs with Answers

1. A clock shows 3:00. What is the angle between the hour hand and the minute hand?

• A. 45 degrees
• B. 60 degrees
• C. 90 degrees
• D. 120 degrees

Explanation: Each hour mark is 30 degrees apart, since 360 divided by 12 is 30, and at three o'clock the hands are three marks apart, giving 90 degrees. The general formula is the absolute value of 30H minus 5.5M. At 3:00 that gives 90 minus 0, confirming the answer.

2. If today is Wednesday, what day will it be after 100 days?

• A. Thursday
• B. Friday
• C. Saturday
• D. Sunday

Explanation: Dividing 100 by 7 gives 14 weeks with a remainder of 2, so the day advances by two from Wednesday to Friday. Only the remainder matters, because whole weeks return to the same day. This remainder method solves every calendar question of this type.

3. A man is 24 years older than his son. In two years, his age will be twice that of his son. What is the son's present age?

• A. 20 years
• B. 22 years
• C. 24 years
• D. 26 years

Explanation: Let the son be x, so the father is x plus 24, and in two years x plus 26 equals twice x plus 2, that is 2x plus 4. Solving gives x equal to 22. Checking, the son will be 24 and the father 48, which is exactly double.

4. A shopkeeper sells an item for Rs. 240 at a profit of 20 per cent. What was the cost price?

• A. Rs. 192
• B. Rs. 200
• C. Rs. 220
• D. Rs. 288

Explanation: The selling price is 120 per cent of the cost, so the cost is 240 multiplied by 100 and divided by 120, giving Rs. 200. Taking 20 per cent off the selling price gives Rs. 192, which is the standard trap because percentages are calculated on the cost, not the sale. Checking, 20 per cent of 200 is 40, and 200 plus 40 is 240.

5. If 5 workers build a wall in 12 days, how long would 6 workers take, working at the same rate?

• A. 10 days
• B. 14 days
• C. 12 days
• D. 15 days

Explanation: The total work is 5 multiplied by 12, that is 60 worker days, and dividing by 6 workers gives 10 days. More workers means fewer days, an inverse proportion, so an answer larger than 12 must be wrong at a glance. Checking the direction of the relationship first prevents most errors here.

6. A train 150 m long travelling at 90 km per hour takes how long to pass a stationary pole?

• A. 4 seconds
• B. 6 seconds
• C. 10 seconds
• D. 15 seconds

Explanation: Converting 90 km per hour by multiplying by 5 and dividing by 18 gives 25 m per second, and 150 divided by 25 is 6 seconds. To pass a pole the train covers only its own length, whereas passing a platform would require its length plus the platform's. Forgetting the unit conversion is the usual mistake.

7. The average of five numbers is 20. If one number is removed, the average of the rest is 22. What was the number removed?

• A. 12
• B. 14
• C. 10
• D. 8

Explanation: The original total is 5 multiplied by 20, that is 100, and the remaining four total 4 multiplied by 22, which is 88, so the removed number is 12. Working with totals rather than averages is what makes these questions straightforward. The removed value is below the average, which is why the average of the rest rose.

8. In a group of 40 students, 25 study biology and 20 study chemistry. If every student studies at least one of the two, how many study both?

• A. 5
• B. 10
• C. 15
• D. 20

Explanation: By the inclusion exclusion principle, 25 plus 20 minus both equals 40, so both equals 5. The overlap is counted twice in the simple sum, which is why it must be subtracted once. Drawing two overlapping circles makes the relationship visible.

9. A tank is filled by one pipe in 6 hours and emptied by another in 12 hours. If both are opened together, how long will the tank take to fill?

• A. 8 hours
• B. 12 hours
• C. 6 hours
• D. 18 hours

Explanation: In one hour the filling pipe adds one sixth and the emptying pipe removes one twelfth, giving a net gain of one twelfth per hour, so the tank fills in 12 hours. Working in fractions of the job per unit time is the standard method for pipe and cistern problems. If the outlet were faster than the inlet, the tank would never fill at all.

10. What is the next number in the series 2, 6, 12, 20, 30, ?

• A. 36
• B. 40
• C. 42
• D. 44

Explanation: The differences are 4, 6, 8 and 10, rising by two each time, so the next difference is 12 and the next term is 42. The same series can be written as n multiplied by n plus 1, giving 6 times 7 for the sixth term. Checking a pattern two ways is a good way to confirm it.