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Explanation

Explanation

Let two angles be x and 2x

Given that, angles are supplementary

∴x+2x=180o

 ⇒3x=180

⇒x= 3

180o

 ⇒x=60 o

 Therefore, bigger angle is 2x=120∘

Explanation

Given proportion:

2 : 7 :: 14 : x

We can set up an equation based on the proportion:

2/7 = 14/x

Cross-multiplying:

2x = 14 × 7

2x = 98

Dividing both sides by 2:

x = 98/2

x = 49

Explanation

Explanation

Total parts = 2 + 3 + 5 = 10

Salma's share = (2/10) × 2000 = 400.

Explanation

The sum of the ratio parts is 4 + 6 = 10.

Explanation

Given:

(x + 5) : (x + 7) = 5 : 7

We can write it as:

(x + 5) / (x + 7) = 5/7

Cross-multiplying:

7(x + 5) = 5(x + 7)

7x + 35 = 5x + 35

7x - 5x = 35 - 35

2x = 0

x = 0

Explanation

Let's find the fourth proportional.

If 8 : 4 :: 2 : x, then

8/4 = 2/x

2 = 2/x

x = 1

Explanation

To express 27 minutes 30 seconds and 1 hour in ratio:

Step 1: Convert both times to seconds

27 minutes 30 seconds = (27 * 60) + 30

= 1620 + 30

= 1650 seconds

1 hour = 60 minutes = 60 * 60

= 3600 seconds

Step 2: Calculate the ratio

Ratio = 1650 : 3600

To simplify, divide both parts by their greatest common divisor, which is 150:

= (1650 / 150) : (3600 / 150)

= 11 : 24

Explanation

In inverse proportion, when one quantity increases, the other decreases in the same ratio.

Their product remains constant: x × y = constant.