Explanation

For 2x² - 3x + 1 = 0:  

Sum = 3/2, Product = 1/2  

Let roots be α, β. Then new roots are 1/α, 1/β  

New sum = 1/α + 1/β = (α + β)/αβ = (3/2) / (1/2) = 3  

New product = 1/αβ = 1/(1/2) = 2  

New equation: x² - (sum)x + product = x² - 3x + 2 = 0  

So a:b:c = 1:-3:2

Last verified on 06-05-2026

Explanation

Make b the same in both ratios  

a:b = 3:4  

b:c = 2:5 → multiply by 2 → b:c = 4:10  

Now a:b:c = 3:4:10  

So a:c = 3:10

Last verified on 04-05-2026

Explanation

For similar triangles: area ratio = (side ratio)²  

(side ratio)² = 9/16  

side ratio = √9/16

side ratio = 3/4

Last verified on 04-05-2026

Explanation

Step 1: Let the numbers be

$$8x\text{ and }3x$$

Step 2: Use the difference

8x−3x=20
$$5x=20\Rightarrow x=4$$

Step 3: Find the numbers

$$8x=32,$$

$$3x=12$$

$$Last\; updated\; by\; NA\; on\; 24-April-2026$$

Explanation

Given:

Total students = 500
Present students = 300

Step 1: Find absent students

$$\text{Absent}=500-300=200$$

Step 2: Form ratio (Present : Absent)

$$300:200$$

Step 3: Simplify the ratio

Divide both by 100:

$$3:2$$

Explanation

Step 1: Understand the ratio

Boys : Girls = 3 : 2
Total parts = 3 + 2 = 5

Step 2: Find value of one part

$$frac{25}{5} = 5$$

Step 3: Find number of boys

$$3\times 5=15$$

Explanation

Two quantities are in inverse proportion when one increases and the other decreases.

Their product always remains constant.

Common in real-life situations like speed & time.

If one doubles, the other becomes half.

It is also called indirect proportion.

Direct Proportion → Both increase or decrease together.

Last verified on 12-04-2026

Explanation

Let Milk = 3k, Wheat = 2k  

Wheat increases by 50%: new Wheat = 2k × 1.5 = 3k  

New ratio Milk : Wheat = 3k : 3k = 1 : 1  

Last verified on 12-04-2026

Explanation

If wheat = 100

Then sugar = 100% more = 100 + 100 = 200

So sugar : wheat = 200 : 100 = 2 : 1

Last verified on 11-04-2026

Explanation

Red : Blue = 3 : 2

If 3 parts = 21 red marbles  

Then 1 part = 21 ÷ 3 = 7

So blue = 2 parts = 2 × 7 = 14

Last verified on 11-04-2026