BPSC CCE Prelims
Numerical Ability Previous Year Questions (PYQs)
Showing solved Previous Year Questions for Chapter: Numerical Ability
Topic Breakdown: Scroll →
At what time between 2 and 3 O'Clock will the hands of a clock be together?
Detailed Explanation:
Concept: Clock hands coincide when the minute hand catches up to the hour hand.
At 2:00, the hour hand is at 60° (2 × 30°/hour). The minute hand moves at 6°/minute, the hour hand at 0.5°/minute.
After t minutes: 6t = 60 + 0.5t → 5.5t = 60 → t = 120/11 = 1010/11 minutes past 2.
What should come in place of ? in the following series?
117, 98, 80, 64, ?, 42
Detailed Explanation:
Pattern: The series decreases with differences that increase by +1 each time.
Differences: 117 → 98 is −19, 98 → 80 is −18, 80 → 64 is −16.
Next difference: Pattern shows increments of +1, +2, +3, so next is −16 + 3 = −13.
Missing term: 64 − 13 = 51.
Verification: 51 → 42 is −9 (increase of +4 from −13), confirming the pattern.
If + means ×, × means −, ÷ means + and − means ÷, then 175 − 25 ÷ 5 + 20 × 3 + 10 equals to:
Detailed Explanation:
Given substitutions: − means ÷, ÷ means +, + means ×, × means −
Original expression: 175 − 25 ÷ 5 + 20 × 3 + 10
After substitution: 175 ÷ 25 + 5 × 20 − 3 × 10
Apply BODMAS:
Division first: 175 ÷ 25 = 7
Multiplication: 5 × 20 = 100 and 3 × 10 = 30
Addition and subtraction: 7 + 100 − 30 = 77
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Rahul is 3 times as old as Seema. Laxmi was twice as old as Rahul four years ago. In four year's time, Rahul will be 31. What are the present ages of Seema and Laxmi?
Detailed Explanation:
Rahul's present age: In 4 years he will be 31, so currently 31 − 4 = 27 years.
Seema's present age: Rahul is 3 times as old as Seema, so Seema = 27 ÷ 3 = 9 years.
Laxmi's present age: Four years ago Rahul was 23 years (27 − 4), and Laxmi was twice that age = 46 years. Currently Laxmi = 46 + 4 = 50 years.
How many times do the hands of a clock coincide in a day?
Detailed Explanation:
Concept: The minute hand moves 12 times faster than the hour hand.
In a 12-hour period, the hands coincide 11 times (at 12:00, ~1:05, ~2:11, ~3:16, ~4:22, ~5:27, ~6:33, ~7:38, ~8:44, ~9:49, ~10:55).
The next coincidence at 12:00 marks the start of the next cycle, so it is not counted twice.
In a 24-hour day (two 12-hour cycles): 11 × 2 = 22 coincidences.
If ÷ means +, − means ÷, × means −, and + means ×, then the value of:(36×4)−8×44+8×2+16÷1\(\frac{(36\times 4)-8\times 4}{4+8\times 2+16\div 1}\) is
Detailed Explanation:
Step 1 – Replace operators: ÷ becomes +, − becomes ÷, × becomes −, + becomes ×
Numerator: (36×4)−8×4 becomes (36−4)÷8−4 = 32÷8−4 = 4−4 = 0
Denominator: 4+8×2+16÷1 becomes 4×8−2×16+1 = 32−32+1 = 1
Final value: 0÷1 = 0 (Option 2)
If February 1, 1996, is Wednesday, what day is March 3, 1996?
Detailed Explanation:
1996 is a leap year, so February has 29 days.
From February 1 to March 3: (29 − 1) days in February + 3 days in March = 31 days.
31 days = 4 weeks + 3 days, so Wednesday + 3 days = Saturday.
How many words, no matter if they are meaningless, can be formed by the letters of the word 'DIARY'?
Detailed Explanation:
The word 'DIARY' contains 5 distinct letters (D, I, A, R, Y).
The number of arrangements (permutations) of 5 distinct letters = 5! = 5 × 4 × 3 × 2 × 1 = 120.
Since 120 is not listed among options 1, 2, or 3, and option 4 states "More than one of the above" (which is also incorrect as none of the values 24, 5, or 10 equals 120), the correct answer is Option 5: "None of the above".
A rectangle has an area 30 cm2 and perimeter 26 cm. Its sides (in cm) are
Detailed Explanation:
Let length = l cm and breadth = b cm.
Area equation: l × b = 30
Perimeter equation: 2(l + b) = 26 ⇒ l + b = 13
From l + b = 13, we get b = 13 - l. Substituting in l × b = 30:
l(13 - l) = 30 ⇒ 13l - l² = 30 ⇒ l² - 13l + 30 = 0
Factoring: (l - 10)(l - 3) = 0 ⇒ l = 10 or l = 3
If l = 10, then b = 3; if l = 3, then b = 10.
The sides are 10 cm and 3 cm.
A shopkeeper offers 10% discount on an item with marked price 400. If he charges 10% GST, then the final price of the item is
Detailed Explanation:
Marked Price (MP) = ₹400
Discount (10%) = 10% of 400 = ₹40
Discounted Price = 400 - 40 = ₹360
GST (10%) is charged on the discounted price = 10% of 360 = ₹36
Final Price = 360 + 36 = ₹396
Reshma donates one-fourth of her property to a charity organization and divides the remaining property equally among her three children. The part of property each child gets is
Detailed Explanation:
Reshma donates 1/4 of her property, leaving 3/4 remaining.
Dividing equally among 3 children: Each child receives (3/4) ÷ 3 = 3/12 = 1/4 of the total property.
A clock is set right at 6 a.m. It gains 10 minutes in 24 hours. What will be the right time when the clock indicates 11 a.m. on the next day?
Detailed Explanation:
The clock gains 10 minutes in 24 real hours, so in 24 real hours it shows 24 hours 10 minutes. From 6 a.m. to 11 a.m. next day = 29 hours on the fast clock.
If the clock shows 29 hours, real time elapsed = 29 ÷ (24 + 10/60) = 29 ÷ (1450/60) = (29 × 60)/1450 × 24 = 28 hours 48 minutes. Adding this to 6 a.m. gives 10:48 a.m.
Therefore, the correct time is 48 minutes past 10, making Option 1 the correct answer.
At what time between 5 and 6 will the two hands of a watch coincide?
Detailed Explanation:
The hour and minute hands of a clock coincide when the angle between them is 0°. At 5 o'clock, the hour hand is at 150° (30° × 5). The minute hand moves at 6° per minute, while the hour hand moves at 0.5° per minute, creating a relative speed of 5.5° per minute.
To close the 150° gap: M = 150 ÷ 5.5 = 300/11 = 27³⁄₁₁ minutes. This can also be derived using the standard formula for hand coincidence: M = (60H)/11, where H = 5.
Therefore, the hands coincide at 27³⁄₁₁ minutes past 5, making Option 2 the correct answer.
Anil and Suman together can do a work in 12 days, which Anil alone can do in 20 days. If Suman alone has to do this work, he will take
Detailed Explanation:
Anil's rate: 1/20 work per day. Together rate: 1/12 work per day. Suman's rate = 1/12 − 1/20 = (5−3)/60 = 2/60 = 1/30 work per day.
Alternatively, using combined work formula: (20×y)/(20+y) = 12 → 20y = 240 + 12y → 8y = 240 → y = 30.
Therefore, Suman alone takes 30 days, making Option 3 the correct answer.
In a class of 55 students, 34 like to play Cricket and 26 like to play Badminton. Also, each student likes to play at least one of the two games. How many students like to play both Cricket and Badminton?
Detailed Explanation:
Apply the set theory formula: Total = Cricket + Badminton − Both. Given 55 students total, 34 like cricket, 26 like badminton, and each student plays at least one game.
Substitute: 55 = 34 + 26 − Both ⇒ Both = 60 − 55 = 5 students.
Therefore, 5 students like both games, making Option 2 the correct answer.