The difference between the compound and simple interest = P × (R/100)²

ATQ, 2.25P = P × (R/100)²

^⇒ R² = 22500

⇒ R= 150%

The simple interest on the same sum at the same rate of interest after one year is = (S - 2.25P) Rs.

⇒ (P × 150 × 1)/100 = S - 2.25P

⇒ 1.5P = S - 2.25P

⇒ S = 3.75P ...(I)

The compound interest on the same sum at the same rate of interest after 2 years = P × [(1 + (150/100))² - 1] = 5.25P

Using (I)

Required CI = 5.25 × (S/3.75) = 1.4S Rs.

Hence, the correct answer is 1.4S Rs.

Given:

The average of three numbers = 16.

Two of the numbers are 18 and 12.

Formula used:

Average = Sum of observations/Number of observations

Calculation:

Let the third number be x

According to the question,

16 = (18 + 12 + x)/3

⇒ 18 + 12 + x = 16 × 3

⇒ 30 + x = 48

⇒ x = 18

∴ The third number is 18.

Area of the circle=πr²

2464 = 22/7 * r²

Radius of the circle=28 cm

Circumference of the circle = 2 * π* r = 2 * 22/7 * 28 

= 176 cm

Breadth of the rectangle = 6/7 * 28=24 cm

Perimeter of the rectangle = 2 * (l + b)

176 = 2 * (l + 24)

Length of the rectangle=64 cm

Area of the rectangle = l * b=24 * 64=1536 cm²

Given:

Total number of males in all five places = 35 + 32 + 30 + 45 + 40 = 182

Total number of females in all five places = 28 + 40 + 35 + 42 + 32 = 177

Formula:

x as a percent of y = x/y × 100

Calculation:

Percentage of the total number of females in all five places approximately the total number of males in all five places is = (177/182) × 100 = 97%

Given:

A invested (2X + 1) lakhs and B invested (4X + 9) lakhs in a partnership of 28 months and 30 months respectively

The ratio of their profits after their respective time period is 2:5

Formula used:

Profit = Investment × Time

Calculation:

According to the question,

Let’s carefully recheck step by step ✅

Cheaper rice = ₹60/kg

Costlier rice = ₹67.5/kg

Mean price = ₹64/kg

Using alligation rule:

So,

That means cheaper rice : costlier rice = 7:8.

But the question asks: In what ratio should rice costing ₹67.5 (costlier) be mixed with rice costing ₹60 (cheaper)?

That means we need Costlier : Cheaper, i.e. the reverse of above.

So the ratio = 8 : 7 ✅

Correct Answer: 8:7 ✔️

Step 2: Divisibility by 11

Rule: (Sum of digits in odd places) − (Sum of digits in even places) must be divisible by 11.

Number = 1 5 x 1 y 2

Given:

Radius = 5.5 cm

Total height of the structure = 32.3 cm

Height of the cylinder = 19.1 cm

Formula used:

The surface area of the cone = π × radius × slant height

The surface area of the cylinder = 2 × π × radius × height

Calculation:

Radius = 5.5 cm

Height of the conical part = 13.2 cm

Slant height of the conical part = √(Radius² + Height²)

⇒ √(5.5² + 13.2²) = √(30.25 + 174.24)

⇒ √(204.49) = 14.3 cm

∴ The surface area of the structure = Surface area of the conical part + surface area of the cylindrical part

⇒ π × radius × slant height of conical part + 2 × π × radius × height of the cylindrical part

⇒ (22/7 × 5.5 × 14.3) + (2 × 22/7 × 5.5 × 19.1)

⇒ 22/7 × 5.5 × (14.3 + 2 × 19.1)

⇒ 22/7 × 5.5 × 52.5 = 22 × 5.5 × 7.5

⇒ 907.5 cm²

∴ The Surface area of the structure is 907.5 cm².

✅ Final Answer: 119/10