Explanation

Make B common in both ratios:

A:B = 2:3 → multiply by 4 → A:B = 8:12

B:C = 4:5 → multiply by 3 → B:C = 12:15

Now combine:

A:B:C = 8:12:15

Last verified on 10-05-2026

Explanation

Let present ages: father = 9k, son = 2k

After 12 years:  

father = 9k + 12  

son = 2k + 12  

Ratio = 3:1

So (9k + 12)/(2k + 12) = 3/1  

9k + 12 = 3(2k + 12)  

9k + 12 = 6k + 36  

9k - 6k = 36 - 12  

3k = 24  

k = 8

Present age of son = 2k = 2 × 8 = 16 years

Last verified on 10-05-2026

Explanation

a:b = 6:7 and b:c = 7:8  

Since b is 7 in both ratios, we can join them directly:  

a:b:c = 6:7:8  

So a:c = 6:8  

Simplify: 6:8 = 3:4

Last verified on 09-05-2026

Explanation

a : b = 5 : 6  

b : c = 2 : 3 = 6 : 9  

So a : b : c = 5 : 6 : 9  

Therefore a : c = 5 : 9  

Last verified on 08-05-2026

Explanation

Make b the same in both ratios:  

a : b = 4 : 5 = 12 : 15

b : c = 3 : 2 = 15 : 10

So a : b : c = 12 : 15 : 10

Therefore a : c = 12 : 10 = 6 : 5

Last verified on 07-05-2026

Explanation

a : b = 2 : 3

b : c = 3 : 4

Since the value for b is 3 in both, just chain them:  

a : b : c = 2 : 3 : 4

Last verified on 06-05-2026

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

$$8x=32,$$

$$3x=12$$

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