This question requires a basic subtraction operation involving decimals.
To find out how much money is left, you need to subtract the amount spent from the initial amount Akbar had.
Initial money = $12.00
Money spent = $8.40
Money left = $12.00 - $8.40
Performing the subtraction: $12.00 - $8.40 = $3.60.
Option C: $3.60 is the correct answer.
Options A, B, and D are incorrect results, likely due to errors in decimal subtraction or borrowing during the calculation. Always align the decimal points when subtracting numbers with decimals.
To find the square of the distance between two points A(x1, y1) and B(x2, y2), we use the distance formula squared: d2 = (x2 - x1)2 + (y2 - y1)2. For points A(4, -1) and B(3, 5):
(3 - 4)2 = (-1)2 = 1
(5 - (-1))2 = (5 + 1)2 = 62 = 36
Adding these values gives 1 + 36 = 37. Options A, C, and D are incorrect calculations, likely resulting from errors in applying the formula or arithmetic mistakes.
A tangent is a straight line that touches a curve or a curved surface at a single point, without crossing it. A circle is a continuous curve composed of an infinite number of points along its circumference. Since a unique tangent line can be drawn at every single point on the circle's circumference, and there are infinitely many points on a circle, it follows that an infinite number of tangents can be drawn to a circle. Options A, B, and C suggest a finite number, which contradicts the continuous nature of a circle.
To calculate the distance covered, we use the formula: Distance = Speed × Time. The speed is given as 55 km/h, and the time is 12 minutes. First, convert the time from minutes to hours:
12 minutes ÷ 60 minutes/hour = 0.2 hours
Now, multiply the speed by the time:
Distance = 55 km/h × 0.2 h = 11 km
Therefore, the car will cover 11 km in 12 minutes. Options A, B, and D are incorrect, likely due to errors in unit conversion or calculation.
To find the share of the third partner, first simplify the given ratio 4/3:7/6:11/12. The least common multiple (LCM) of the denominators (3, 6, 12) is 12. Multiplying each fraction by 12 gives us the simplified ratio: (4/3)*12 : (7/6)*12 : (11/12)*12 = 16:14:11.
The sum of the ratio parts is 16 + 14 + 11 = 41.
The third partner's share is (11/41) of the total profit.
Share = (11/41) * 12300 = 11 * 300 = 3300.
The other options are incorrect because they do not result from the correct simplification of the ratio and subsequent calculation of the third partner's share.
To determine the number of smaller containers that can be filled, we must calculate the volume of both the large tank and the small containers, ensuring consistent units.
Large Tank: Diameter = 2.4 m = 240 cm, so Radius (R) = 120 cm. Height (H) = 6.4 m = 640 cm. Volume = π * R² * H = π * (120)² * 640 = 9216000π cm³.
Small Container: Radius (r) = 8.2 cm. Height (h) = 28 cm. Volume = π * r² * h = π * (8.2)² * 28 = 1882.72π cm³.
Number of Containers: Divide the large tank's volume by the small container's volume: (9216000π) / (1882.72π) ≈ 4895.19.
Since only complete containers can be filled, the answer is 4895. The 'm³' unit in the option is a mislabeling, as the question asks for a count.
To calculate 80% of 700, you need to understand that 'percentage' means 'per hundred'. Therefore, 80% can be written as the fraction 80/100 or the decimal 0.80.
The calculation is: (80/100) * 700.
This simplifies to 0.80 * 700.
Performing the multiplication gives 560.
The other options are incorrect because they represent different numerical outcomes that would arise from miscalculations, such as using an incorrect percentage value or performing erroneous arithmetic operations.
The other options are incorrect as they would result from errors in the division or multiplication steps, or from incorrectly setting up the percentage calculation.
The given series 11, 13, 17, 19, 23, 29, 31, 37, 41 consists of prime numbers in ascending order. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Following 41, the next prime number is 43. 47 is prime but not next, while 51 and 57 are composite numbers.
By using PEMDAS: Parentheses: Simplify inside the parentheses first. There is nothing to simplify inside the parentheses themselves, but we should identify that
3(2) means
3×2.
3(2)=3×2=6
So the equation becomes:
5+2×6÷6
Multiplication and Division: Next, we perform multiplication and division from left to right.
Let the number be X. The problem states X + 20% of X = 102. This can be written as X + 0.20X = 102, which simplifies to 1.20X = 102. Dividing 102 by 1.20 gives X = 85. Therefore, 85 is the correct number.
The man spends 35% + 25% = 60% initially. Remaining income is 100% - 60% = 40%. He spends 80% of this remaining 40% on rent, which is 0.80 * 40% = 32%. Total spent is 60% + 32% = 92%. Thus, he is left with 100% - 92% = 8% of his income.
"Stand with" means to support someone, fitting the promise of support in all circumstances. "Stand up to" means resist, "stand off" means distance, and "stand by" means ready or adhere, none fitting the context.
The total cost is (3*16) + (4*23) = 48 + 92 = 140. With 7 books in total, the average price is 140/7 = 20. The other options are incorrect calculations.
If the bucket capacity is reduced to two-fifths, then five-halves (2.5) times more buckets are needed. Therefore, 25 buckets * 2.5 = 62.5 buckets are required. Other options are incorrect.
The correct answer is 35. This question follows a simple numerical pattern in which each number is multiplied by one less than itself. For example, 5 = 5 × (5 − 2) = 5 × 3 = 15 and 6 = 6 × (6 − 2) = 6 × 4 = 24. Applying the same rule to 7 gives 7 × (7 − 2) = 7 × 5 = 35. Therefore, the missing value is 35. Such pattern-recognition questions are commonly asked in intelligence and aptitude tests to assess logical reasoning rather than mathematical formulas.
When solving number series or analogy questions, it is important to identify the relationship between the given numbers before attempting the next value. In this case, the multiplier increases by one as the original number increases: 5 × 3 = 15, 6 × 4 = 24, and 7 × 5 = 35. Recognizing this consistent rule leads directly to the correct answer without requiring complex calculations. Pattern-based reasoning is widely tested in competitive examinations because it measures analytical thinking and problem-solving ability.
Why the other options are incorrect:
30 is incorrect because it does not follow the multiplication pattern established by the previous values.
40 is incorrect because no valid mathematical relationship from the given examples produces this result.
45 is incorrect because it does not satisfy the consistent rule of multiplying the number by (number − 2).
All numbers in the given series except 54 are multiples of 5. Therefore, 54 is the odd one out as it does not fit this numerical pattern, unlike 10, 45, or 75.
Units made are proportional to days and machines. (600 units / (9 days * 20 machines)) = (X units / (12 days * 18 machines)). Solving for X gives 720 units, making other options incorrect calculations.
The correct answer is 7 hours and 51 minutes. The train departed Lahore at 9:32 a.m. and arrived in Peshawar at 5:23 p.m. To calculate the travel time, we convert the arrival time to a 24‑hour format: 5:23 p.m. = 17:23. The difference between 17:23 and 09:32 is calculated as follows:
Hours: 17 − 9 = 8 hours
Minutes: 23 − 32 = −9 minutes
We subtract the 9 minutes from the 8 hours, giving 7 hours and 51 minutes.
Options 1 (7 hours), 3 (7 hours 30 mins), and 4 (7 hours 40 mins) do not match the correct arithmetic calculation. Hence, the total journey time is 7 hours and 51 minutes.
When trains move in opposite directions, their relative speed is summed. Convert speeds to m/s and total distance to meters. Time is total distance divided by relative speed, yielding 10.8 seconds.