Let my current age = x years and my cousin’s age = y years.

Three-fifths of my current age is the same as five-sixths of that of one of my cousins’,

⇒ 3x/5 = 5y/6

⇒ 18x = 25y

My age ten years ago will be his age four years hence,

⇒ x – 10 = y + 4

⇒ y = x – 14,

⇒ 18x = 25(x – 14)

⇒ 18x = 25x – 350

⇒ 7x = 350

∴ x = 50 years

Calculation:

Now, the number of American nationals of the age group below 20 years who visited China

⇒ 500000 × 60% × 60%

⇒ 1,80,000

∴ The number of American nationals of the age group below 20 years who visited China is 1,80,000.

Given:

From A to B, speed = d = 30 km/h

From B to A, speed = p = 45 km/h

Concept used:

Average speed = 2dp/(d + p)

Calculation:

Average speed = (2 x 30 x 45)/(30 + 45)

⇒ 2700/75

⇒ 36

Therefore, the correct answer is 36

Given:

The speed of the train = 42 km/h

Formula used:

 Where, S = Speed, D = Distance, and T = Time

Calculation:

Let the length of the platform be X m

According to the question

Given:

The ratio of alpha and beta to age is 2 ∶ 5.

Sum of their ages is 238.

Calculation:

Let's assume the ages of alpha and beta are 2x and 5x, respectively, where x is a common multiplier.

So, we can write the equation:

2x + 5x = 238

7x = 238

Dividing both sides by 7:

x = 238 / 7

x = 34

Now, we can find the ages of alpha and beta:

Alpha's age = 2x = 2 * 34 = 68

Beta's age = 5x = 5 * 34 = 170

The difference between their ages is:

170 - 68 = 102

Therefore, the difference between the ages of alpha and beta is 102.

∴ Option 1 is the correct answer.

Given:

81, 52, 29, 73, 48, 33, 31

Concept used: 

If n is odd, the median is the middle value in the set:

Calculation:

On arranging the given data in decreasing order,

⇒ 81, 73, 52, 48, 33, 31, 29

Total number of observation = 7

⇒ Median = 4th observation

⇒ Median = 48

∴ The median of the above data is 48.

Given:

Mean = 8

Median = 11

Concept used:

Mode = 3 Median - 2 Mean

Calculation:

Mode = 3 × 11 - 2 × 8

⇒ Mode = 33 - 16

⇒ Mode = 17

∴ The mode is 17.

∴ Option 3 is the correct answer.

Given:

The perimeter of a rectangle having area equal to 144 cm2

Sides are in the ratio 4 : 9

Formula Used:

Area of rectangle = l × b

Perimeter of rectangle = 2(l + b)

Calculation:

Let, 'l' and 'b' are the sides of the rectangle.

⇒ b = 4x and l = 9x

Area of rectangle = l × b

⇒ 144 = (4x) × (9x)

⇒ x = 2

Now, b = 4 × 2 = 8 cm and l = 9 × 2 = 18 cm

Perimeter of rectangle = 2(l + b)

⇒ 2(18 + 8) = 2 × 26 = 52 m

Perimeter of rectangle = 52 m

∴ The perimeter of the rectangle is 52 m

GIVEN:

Selling price of the article is Rs. 432

Profit gained on the article is 35%

FORMULA USED:

Selling price = {1 + (Profit %) /100} × Cost Price

CALCULATIONS:

⇒ 432 = {1 + (35/100)} × Cost Price

⇒ Cost Price = 432/ 1.35 = 320

Hence, Cost price of the article is Rs. 320.

Alternate solution

Such questions can be solve easily by assuming Cost price 100x.

Hence, profit = 35x and selling price = 135x

According to question, 

135x = 432

⇒ x = 432/135

∴ Cost price = 100x = (432/135) × 100 = 320.

Given:

Ordinary interest rate = 12% per annum

Time period = 5 years

Interest earned = Rs. 5640

Formula:

Simple Interest S.I. = (PRT)/100

where,

P = Principal amount

R = Rate of interest

T = Time period

Solution:

Let P be the principal amount invested.

Using the formula for simple interest, we have:

⇒ S.I. = (PRT)/100

⇒ 5640 = (P × 12 × 5)/100

⇒ 5640 = (60P)/100

⇒ 564000 = 60P

⇒ P = 9400

Therefore, the amount invested is Rs. 9400.