Explanation

√(13⁴) = √((13²)²)  

= 13²  

= 169

Explanation

To find the smallest fraction among:  

11/13, 9/11, 3/4, 5/7, we compare their decimal values:

- 11 ÷ 13 ≈ 0.846  

- 9 ÷ 11 ≈ 0.818  

- 3 ÷ 4 = 0.75  

- 5 ÷ 7 ≈ 0.714

The smallest fraction is: 5/7 ≈ 0.714

Explanation

Explanation

To simplify the ratio 360 : 270:

Step 1: Find the GCD (Greatest Common Divisor) of 360 and 270.  

GCD of 360 and 270 is 90.

Step 2: Divide both terms by 90:  

- 360 ÷ 90 = 4  

- 270 ÷ 90 = 3  

Simplified Ratio = 4 : 3

Explanation

 Work = Men × Days

So,  

105 men × 45 days = 4725 man-days

Now, if 90 men are doing the same work:

4725 man-days ÷ 90 men

= 52.5 days

Explanation

The square root of 13 is approximately:

√13 ≈ 3.605  

It is an irrational number (cannot be written as an exact fraction).

Explanation

Let A and B’s incomes be 3x and 2x, respectively.  

Let their expenses be 5y and 3y, respectively.  

Their savings = Income − Expense = Rs. 1000 for both.

So:

For A:  

3x − 5y = 1000  → (1)

For B:  

2x − 3y = 1000  → (2)

Multiply (1) by 2:  

6x − 10y = 2000

Multiply (2) by 3:  

6x − 9y = 3000

Now subtract:  

(6x − 10y) − (6x − 9y) = 2000 − 3000  

⇒ −y = −1000  

⇒ y = 1000

Now plug y = 1000 into equation (1):  

3x − 5(1000) = 1000  

⇒ 3x = 6000  

⇒ x = 2000

Now find incomes:  

A's income = 3x = 6000  

B's income = 2x = 4000 

Explanation

5% of 55 =  

(5/100) × 55 = 2.75

Explanation

3% of 2000 = (3/100) × 2000 = 60

Explanation

1% of 2000 =  

(1/100) × 2000 = 20

Now, add 20 three times:  

20 + 20 + 20 = 60