Quantitative Aptitude: Arithmetic and Word Problems

Let first day = x. Total = x + (x+6) + (x+12) + (x+18) + (x+24) = 5x + 60 = 100, so 5x = 40, x = 8. This is an arithmetic progression problem with common difference 6.

19 x 19 x 19 = 6859. This can be calculated as 361 x 19 (since 19x19=361) or memorized as a cube. 19^3 = 6859.

Interest for 3 years (5-2) = 2600-2240 = Rs.360. Annual interest = Rs.120. For 2 years, interest = Rs.240. Principal = 2240-240 = Rs.2000. Rate = 120/2000 = 6%. This uses the constant growth property of simple interest.

A's efficiency is 50% more than B, so A's rate = 1.5 × (1/24) = 1/16. Combined rate = 1/24 + 1/16 = 5/48 work per day. Days needed = 48/5 = 9.6 days. Option D (16 days) is B's time alone, option C (6 days) would require faster workers, and option B (8 days) is too low.

To find what percent of 5/8 is 8/5, calculate (8/5) ÷ (5/8) × 100 = (8/5) × (8/5) × 100 = 64/25 × 100 = 256%. Option A (100) would mean the fractions are equal, option C (64) is the product without multiplying by 100, and option D (1024) is incorrectly squared.

Original work = 6 x 30 x 9 = 1620 man-hours. Ten times that is 16200 man-hours. The new schedule gives 25 x 8 = 200 hours per man, so men needed = 16200 / 200 = 81, matching option C.

To solve this question, the user needs to know how to set up and solve a system of equations. Let the number of girls be x and the number of boys be y. We can then set up two equations based on the given information:

Equation 1: x + y = 45 (the total number of boys and girls is 45)

Equation 2: 0.50x + 1.00y = 39 (the total amount of money distributed is Rs 39)

Now, let's go through each option and see if it satisfies the equations:

A) If there are 10 girls, then there are 35 boys. This satisfies equation 1. The total amount of money given to girls is 0.50 * 10 = Rs 5. The total amount of money given to boys is 1.00 * 35 = Rs 35. The total amount of money distributed is Rs 5 + Rs 35 = Rs 40, which is not equal to Rs 39. Therefore, option A is incorrect.

B) If there are 12 girls, then there are 33 boys. This satisfies equation 1. The total amount of money given to girls is 0.50 * 12 = Rs 6. The total amount of money given to boys is 1.00 * 33 = Rs 33. The total amount of money distributed is Rs 6 + Rs 33 = Rs 39, which is equal to the given total amount. Therefore, option B is correct.

C) If there are 6 girls, then there are 39 boys. This satisfies equation 1. The total amount of money given to girls is 0.50 * 6 = Rs 3. The total amount of money given to boys is 1.00 * 39 = Rs 39. The total amount of money distributed is Rs 3 + Rs 39 = Rs 42, which is not equal to Rs 39. Therefore, option C is incorrect.

D) If there are 18 girls, then there are 27 boys. This satisfies equation 1. The total amount of money given to girls is 0.50 * 18 = Rs 9. The total amount of money given to boys is 1.00 * 27 = Rs 27. The total amount of money distributed is Rs 9 + Rs 27 = Rs 36, which is not equal to Rs 39. Therefore, option D is incorrect.

Thus, the correct answer is:

The Answer is: B) 12.

Total distance is 1600 km. Nagpur is 700 km from Mumbai, so the Mumbai train traveled 700 km and the Calcutta train traveled 900 km in the same time. Their speed ratio is therefore 900:7 = 9:7, matching option D. The other ratios do not reflect these distances.

Let the current be c. Upstream speed = 4.5 - c, downstream = 4.5 + c. Rowing upstream takes twice as long, so 1/(4.5-c) = 2/(4.5+c). Solving gives 4.5 + c = 9 - 2c, so 3c = 4.5 and c = 1.5 km/hr, matching option A.

The relative speed is 12 - 10 = 2 kmph, which is 2000 m per 60 min = 100/3 m per min. To close a 200 m gap takes 200 / (100/3) = 6 minutes, matching option A. The question asks 'after how many hours' but the options are in minutes; the intended answer is 6 min.

Convert A's speed: 36 kmph = 10 m/s, while B is 15 m/s. After 2 minutes (120 s), A covers 10 x 120 = 1200 m and B covers 15 x 120 = 1800 m. The gap is 1800 - 1200 = 600 m, matching option B.

The midpoint is 300 m from each end. A takes 300/6 = 50 s to reach it, while B takes 300/8 = 37.5 s. For them to meet there, B must start 50 - 37.5 = 12.5 s after A. This matches option D.

When A runs 100 m, B runs 90 m and C runs 80 m, so the B:C speed ratio is 9:8. In a 900 m race, when B covers 900 m, C covers 900 x (8/9) = 800 m, so B beats C by 100 m. The phrase about B and C running at the same velocity is inconsistent with the data and can be ignored; the answer 100 m follows from the stated beat margins.

To solve this question, the user needs to have knowledge of the concept of percentages and how to solve for an unknown percentage value.

We can start by using the given information that 84% of a total is 630 marks. We can set up the following equation:

0.84x = 630

Where x is the total number of marks. We can solve for x by dividing both sides by 0.84:

x = 630 ÷ 0.84
x = 750

Therefore, the total number of marks is 750.

Next, we need to find what 90% of 750 is. We can set up the following equation:

0.9 × 750 = 675

Therefore, 90% of the total is equal to 675.

Now, let's go through each option and explain why it is right or wrong:

A. 500: This option is incorrect. 90% of 750 is greater than 500.

B. 550: This option is incorrect. 90% of 750 is greater than 550.

C. 675: This option is correct. We found that 90% of 750 is equal to 675.

D. 425: This option is incorrect. 90% of 750 is greater than 425.

Therefore, the answer is:

The Answer is: C

Both pipes fill the tank: A at 1/36 per hour and B at 1/45 per hour. Combined rate = 1/36 + 1/45 = (5+4)/180 = 9/180 = 1/20 per hour, so the tank fills in 20 hours. The other options do not match the combined rate.

Pipe A fills at 1/36 of the tank per hour and pipe B empties at 1/45 per hour. The net fill rate is 1/36 - 1/45 = (5-4)/180 = 1/180 per hour, so the tank fills in 180 hours. Options 90, 100, and 150 hrs ignore the net rate.

The second of the 9 consecutive numbers is X+1. Interchanging its digits raised the average by 8, so the sum increased by 9 x 8 = 72. Thus the interchanged number minus the original equals 72. For X=18, the second number is 19; 91 - 19 = 72, which fits. Other choices do not produce this difference.

To solve this question, the user needs to know how to find the average of a set of numbers and how to work with consecutive numbers.

The average of a set of numbers is found by adding up all the numbers in the set and then dividing by the total number of numbers.

For a set of consecutive numbers, the average of the set is equal to the middle number.

To find the difference between the averages of the first and last 10 numbers, we need to find the average of the first 10 numbers and the average of the last 10 numbers, and then subtract the former from the latter.

Let's represent the first number by x. Then, the next 29 consecutive numbers will be x+1, x+2, x+3, ..., x+28, x+29.

The average of the first 10 numbers will be the middle number of the set of the first 10 numbers. Since there are 10 numbers, the middle number will be the 5th number. Therefore the average of the first 10 numbers will be:

$$\frac{x + (x+1) + (x+2) + ... + (x+8) + (x+9)}{10} = x + 4.5$$

Similarly, the average of the last 10 numbers will be the middle number of the set of the last 10 numbers. Since there are 10 numbers, the middle number will be the 25th number. Therefore the average of the last 10 numbers will be:

$$\frac{(x+20) + (x+21) + (x+22) + ... + (x+27) + (x+28) + (x+29)}{10} = x + 24.5$$

The difference between the averages of the first and last 10 numbers will be:

$$(x+24.5) - (x+4.5) = 20$$

Therefore, the answer is:

The Answer is: D. 20.

Factorize 1296 = 2^4 x 3^4. The number of factors is found by adding 1 to each exponent and multiplying: (4+1)(4+1) = 25. The other options (20, 35, 15) do not match this divisor count.

If cost price is CP, the marked price is 1.5 x CP. After a 25% discount, selling price = 1.5 x CP x 0.75 = 1.125 x CP, which is a 12.5% profit. The key is to apply the discount to the marked price, not the cost price.