Explanation

Let man required =X

More men, less men (indirect proportion)

M= 15x10/3

M= 150/3

M= 50

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ND19-1-2023

Explanation

Prime Factorization

1050 = 2 × 3 × 5 × 5 × 7

750 = 2 x 3 x 5 x 5 x 5

Common Factor = 2 x 3 x 5 x 5 = 150

Greatest Common Factor (GCF) = 150

Explanation

To solve this problem, you need to use the concept of profit percentage and the formula:

Profit = Selling Price - Cost Price

Given:

Selling Price = Rs. 118

Profit = 50% of Cost Price

Let's calculate the Cost Price:

Profit = (50/100) x Cost Price

Profit = Rs. 118 - Cost Price

Substitute the profit value:

(50/100) x Cost Price = Rs. 118 - Cost Price

Simplify and solve for Cost Price:

Cost Price = Rs. 78.66

Explanation

To find the area of the strip:

1. Calculate the area of the larger rectangle (including the strip):

New length = 82 + 2_4 = 90 cm

New width = 75 + 2_4 = 83 cm

Area of larger rectangle = 90 * 83 = 7470 cm²

2. Calculate the area of the original rectangle:

Area = 82 * 75 = 6150 cm²

3. Find the area of the strip:

Area of strip = Area of larger rectangle - Area of original rectangle

= 7470 - 6150

= 1320 cm²

Explanation

The ratio of boys to girls is given as 3:4, and the total number of students in the class is 28.

Step 1: Add the parts of the ratio

Step 2: Calculate the value of one part

Each part of the ratio represents:

Step 3: Find the number of boys

The boys' share is 3 parts, so:

Explanation

The sum of all odd numbers between 1 and 100 is 50^2=2500

The sum of all even numbers between 2 and 100 is 50^2+50=2550

The total of 1 to 100 natural numbers is 2500+2550

5050

The average of the first 100 numbers is 5050 / 100 = 50.50

Explanation

Discount price=Market price(1-discount price/100)

70=x(1-20/100)

70=x(1-1/5)

70=x(4-1/5)

(70)(5)=4x

350=4x

x=350/4

x=87.5

SH18-8-2023

Explanation

3/4=0.75

5/6=0.833

1/2=0.5

2/3=0.66

4.5=0.8

9/10=0.9

Clearly 0.8 lies between 0.75  and .833

4/5 lies between 3/4 and 5/6 .

Explanation

If A is the father of C and C is the sister of D, then A is also the father of D; since D is the son of B, this means B is the wife of A, making B the sister-in-law of E (A's brother). 

Explanation:

A is the father of C and D are siblings. 

D is the son of B. 

Therefore, B is the mother of D and the wife of A. 

Since E is the brother of A, B becomes E's sister-in-law. 

Explanation

The factors of 16 are 1, 2, 4, 8, and 16, and the prime factorization of 16 is 16 = 2 × 2 × 2 × 2.