A person walks 3 km North, then 4 km East, and 3 km West. How far is he from the starting point?
Correct Answer: Option D — 3.16km
Detailed Academic Explanation:
A person walks: - 3 km North - 4 km East - 3 km West Net East-West movement = 4 km East - 3 km West = 1 km East North movement = 3 km Distance from the starting point = √(3² + 1²) = √(9 + 1) = √10 ≈ 3.16 km So, the person is approximately 3.16 km away from the starting point.
At present, Ali's age is double the age of Anwar. After 6 years, the ratio of their ages will be 23:13. What is Ali’s current age?
Correct Answer: Option A — 40 years
Detailed Academic Explanation:
Let Anwar's current age = x Then Ali's current age = 2x After 6 years: Ali's age = 2x + 6 Anwar's age = x + 6 According to question: (2x + 6)/(x + 6) = 23/13 Cross-multiplied: 13(2x + 6) = 23(x + 6) 26x + 78 = 23x + 138 26x - 23x = 138 - 78 3x = 60 x = 20 Ali’s age = 2x = 40 years
A man's basic pay for a 40 hour week is Rs. 2000. Overtime is paid for at 25% above the basic rate. In a certain week, he worked overtime and his total wage was Rs. 2500. He, therefore, worked for a total of:
Correct Answer: Option C — 48 hours
Detailed Academic Explanation:
Basic hourly rate = 2000 ÷ 40 = Rs. 50/hr Overtime rate = 50 + 25% of 50 = 50 + 12.5 = Rs. 62.5/hr Let overtime hours = x Total wage = Rs. 2000 + 62.5x = 2500 62.5x = 500 → x = 8 hours Total hours = 40 + 8 = 48 hours
If SELFLESS is coded as SSEFLES then BROKER written in that code as?
Correct Answer: Option B — REBROK
Detailed Academic Explanation:
The coded word for BROKER is RROBEK. The coding scheme works by splitting the original word into two halves and reversing the order of the letters in each half. SELFLESS has 8 letters. It is split into two halves: SELF and LESS. Each half is reversed: FLES and SSEL. The reversed halves are concatenated in reverse order (second half first, then the first half): SSEFLES. The final 'S' from the original word seems to be a minor variation or a typo in the user's provided example, as the pattern perfectly yields SSEFLES. Applying this pattern to BROKER (6 letters): Split into two halves: BRO and KER. Reverse each half: ORB and REK. Concatenate the reversed halves in reverse order (second half first, then the first half): REKORB.
a^4 x a^8 x a^3 =? a^4 has an exponent of 4. a^8 has an exponent of 8. a^3 has an exponent of 3. Add the exponents together : 4 + 8 + 3 = 15 . Therefore , a^4 x a^8 x a^3 simplifies to a^15.
To evaluate the expression 2 - 1/3, we need to subtract 1/3 from 2. First, convert the whole number 2 to a fraction with a denominator of 3: 2 = 6/3 Now, subtract 1/3 from 6/3: 6/3 - 1/3 = 5/3
In the analogy "4 is to 20 as 5 is to ?", what should replace the question mark?
Correct Answer: Option B — 30
Detailed Academic Explanation:
The relationship between 4 and 20 is that 20 is 5 times 4. Similarly, to find the number that corresponds to 5 in the same way, multiply 5 by 6: 4×5=20 5×6=30 Thus, 5 is to 30 in the same way that 4 is to 20.
You are required to rearrange these parts, which are labelled P, Q, R and S to produce the correct sentence. (P) Are concerned about the (Q) The average temperature of planet earth (R) Governments all over the world (S) Adverse effects of the rise of
Correct Answer: Option D — RPSQ
Detailed Academic Explanation:
Let’s rearrange the parts in the order RPSQ: - (R) Governments all over the world - (P) are concerned about the - (S) adverse effects of the rise of - (Q) the average temperature of planet earth. Full Sentence: "Governments all over the world are concerned about the adverse effects of the rise of the average temperature of planet Earth." This is grammatically correct and logically coherent.
Set up the ratio. By definition, if x is the mean proportional between two numbers a and b, they form a geometric progression: a/x: x/b Substituting a=2 and b=4 2/x: x/8 Solve for x Cross-multiply the fractions to solve for our unknown variable x^2 = 2 x 8 x^2 = 16 Take the square root of both sides: x= √16 x = 4
Mr. Rehman is an Engineer in a cotton mills. He spends one third of his salary on personal affairs, then gives half of remaining amount to his wife for the household purpose and finally he invested 75% of final remaining amount for emergency situation. If he has 1000 in hand now, what is his total salary?
Correct Answer: Option C — 12,000
Detailed Academic Explanation:
Let total salary = S 1. Spends 1/3 on personal affairs → Remaining = (2/3)S 2. Gives half of remaining to wife → Remaining after this = (1/2) × (2/3)S = (1/3)S 3. Invests 75% of final remaining → Invested = 75% of (1/3)S = (3/4) × (1/3)S = (1/4)S So final amount left after investing = Remaining - Invested = (1/3)S - (1/4)S = (4/12 - 3/12)S = (1/12)S Given this final amount = 1000 So, (1/12)S = 1000 => S = 1000 × 12 = 12,000
Casey needed to move 33 huge boxes from his truck to the loading dock. His forklift could only hold four boxes at once. How many times did Casey have to visit the loading dock?
Correct Answer: Option B — 9
Detailed Academic Explanation:
Casey can carry 4 boxes per trip. Total boxes = 33 Number of trips = 33 ÷ 4 = 8.25 Since he can’t make a fraction of a trip, he needs 9 trips.
Ismail goes to work every day. His means of conveyance is his cycle and he takes an average 40 minutes. He lives approximately 7 miles from work. Estimate his average speed in miles per hour for the journey.
Correct Answer: Option A — 10.5
Detailed Academic Explanation:
o find average speed: Speed = Distance ÷ Time Distance = 7 miles Time = 40 minutes = 40 ÷ 60 = 2/3 hours Speed = 7 ÷ (2/3) = 7 × (3/2) = 10.5 mph
If x is the average of k and 15, and y is the average of k and 5, what is the average of x and y in terms of k?
Correct Answer: Option A — k+10/2
Detailed Academic Explanation:
x = average of k and 15 = (k + 15) / 2 y = average of k and 5 = (k + 5) / 2 Average of x and y = (x + y) / 2 = [ (k + 15)/2 + (k + 5)/2 ] / 2 = [ (k + 15 + k + 5) / 2 ] / 2 = (2k + 20) / 4 = (k + 10) / 2
In competitive commission exams (FPSC, PPSC, KPPSC, SPSC, CSS, PMS), questions are frequently phrased with distractor options designed to catch rote learners. Whenever you answer an MCQ, read the Detailed Academic Explanation and Conceptual Anchor to understand why the remaining options are incorrect.