Math Puzzles and Word Problems

The sequence is based on the squares of numbers 1-5 with their digits reversed: 01^2=01 (10), 02^2=04 (40), 03^2=09 (90), 04^2=16 (61). The next is 05^2=25, which reversed is 52.

Let N be total steps and v be escalator speed in steps per second. When Brian runs 6 steps, escalator moves N-6 steps in 39 seconds: N-6 = 39v. When he runs 13 steps, escalator moves N-13 steps in 28.5 seconds: N-13 = 28.5v. Subtracting: 7 = 10.5v, so v = 2/3 steps/sec. Then N = 39v + 6 = 39(2/3) + 6 = 26 + 6 = 32 steps. Time without running: t = N/v = 32/(2/3) = 48 seconds.

Let grandson's age be g, son's age be s, and your age be y. Grandson's days = son's weeks means g365 = s52, so g ≈ s/7. Grandson's months = your years means g12 = y. Also g + s + y = 100. Substituting y = 12g and s ≈ 7g: g + 7g + 12g = 100, so 20g = 100, g = 5. Therefore y = 125 = 60 years.

First convert speed: 60 km/h = 60 × (1000/3600) = 16.67 m/s. Distance covered in 30 seconds = 16.67 × 30 = 500 m. This distance equals train length + bridge length, so bridge = 500 - 77 = 423 m. The train's length must be added to the bridge length when calculating total crossing distance.

To solve this question, the user needs to know basic arithmetic and the concept of multiplication. The user must divide 6909 by 147 to find the correct answer.

We can solve the equation as follows:

X * 147 = 6909

X = 6909 / 147

X = 47

Therefore, the correct answer is option B.

Explanation for each option:

A. 37: This option is incorrect because it is the result of dividing 6909 by 187 instead of 147.

B. 47: This option is correct because it is the result of dividing 6909 by 147.

C. 27: This option is incorrect because it is the result of dividing 6909 by 257 instead of 147.

D. 67: This option is incorrect because it is the result of dividing 6909 by 167 instead of 147.

The Answer is: B

To solve this problem, the user needs to know basic arithmetic and the concept of percentages and division. The user must multiply 1000 by 45%, then divide the result by 10.

First, let's calculate 1000 multiplied by 45%:
1000 x 45% = 1000 x 0.45 = 450

Next, let's divide 450 by 10:
450 / 10 = 45

Therefore, the answer is 45, which is option B.

Option A (35) is incorrect because it is not the correct result of the calculation.

Option B (45) is correct because it is the result of the calculation.

Option C (3.5) is incorrect because it is not the correct result of the calculation.

Option D (4.5) is incorrect because it is not the correct result of the calculation.

The Answer is: B. 45

Using the formula P = A / (1 - r)^n: P = 29644.032 / (0.88)^3. 0.88 cubed is 0.681472. 29644.032 / 0.681472 = 43,500. The machine was purchased for Rs. 43,500.

Let initial men = M. After 10 days, 40 days of food remains for M men: total food = 40M. With 500 more men (M+500), this lasts 35 days: 40M = 35(M+500). Solving gives 5M = 17500, so M = 3500.

Let the number be x. "Exceeds 20% of itself by 40" means x = 0.2x + 40. Solving: 0.8x = 40, so x = 50.

The ratio is 4:3:5. The lowest part is 3 units, which equals Rs. 12,000. Therefore, 1 unit = 4,000. The total ratio is 4+3+5 = 12 units. Total money = 12 * 4,000 = Rs. 48,000.

LCM of 3,4,5,6,8 = 2^3 × 3 × 5 = 120. For a perfect square, all prime exponents must be even. Multiply by 2 × 3 × 5 = 30 to get 3600.

HCF = 12 means 12 is the largest number dividing all three. In ratio 1:2:3, the smallest number must equal the HCF, so numbers are 12, 24, 36.

To find the square root of 4761, note that it ends in 1, so the root must end in 1 or 9. Since 60 squared is 3600 and 70 squared is 4900, the root must be 69.

First, calculate the sum on the left: 17 + 47 = 64. The equation is 64 = 7 + x. Subtracting 7 from 64 gives 57.

To solve: 33 + 18 = 51, so 29 + ? = 51. Therefore, 51 - 29 = 22. The answer is 22. This is a basic arithmetic equation requiring you to find the missing number that balances both sides.

First, calculate the sum on the left: 56 + 81 = 137. The equation is 137 = 44 + x. Subtracting 44 from 137 gives 93.

First, calculate the left side: 54 - 32 = 22. The equation becomes 22 = 25 - x. Solving for x, we get x = 25 - 22, which equals 3.

To solve 1/4 + x = 3/4, subtract 1/4 from both sides. x = 3/4 - 1/4 = 2/4. Simplifying the fraction 2/4 results in 1/2.

To solve 3/5 × ? = 2/5, divide both sides by 3/5: ? = (2/5) ÷ (3/5) = (2/5) × (5/3) = 2/3. Multiplying 3/5 by 2/3 gives (3×2)/(5×3) = 6/15 = 2/5, which checks out.

60% of 120 means 60/100 × 120. Simplify: 0.60 × 120 = 72. You can also calculate it as 60% of 100 = 60 plus 60% of 20 = 12, giving 72 total.