Question

The ratio between two numbers is 3: 4. If each number is increased by 2, then ratio becomes 7:9. Hence the numbers (A) 24, 32 (B) 12, 16 (C) 6, 8 (D) 16, 12

Answer 1

Let the common be x
A/q
3x+2÷ 4x+2 = 7/9
27x+18= 28x+14
X = 4
Hence the numbers are...
3*4=12
And 4*4= 16

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Answer 2

Answer:

The correct option is B. (12,16)

Step-by-step explanation:

Let the two numbers be x and y

Now, x : y = 3 : 4

$\implies \frac{x}{y}=\frac{3}{4}\\\\\implies 4\cdot x-3\cdot y=0......(1)$

When each number is increased by 2, then the ratio becomes 7 : 9

$\implies \frac{x+2}{y+2}=\frac{7}{9}\\\\\implies 9\cdot x-7\cdot y+4=0....(2)$

Now, solving (1) and (2) :

$\text{Putting }x=\frac{3}{4}\cdot y \text{ in equation (2) we get }\\\\9\cdot (\frac{3}{4}\cdot y)-7\cdot y+4=0\\\\\implies \frac{27}{4}\cdot y-7\cdot y+4=0\\\\\implies \frac{27\cdot y-28\cdot y+16}{4}=0\\\\\implies -y+16=0\\\bf\implies y=16\\\\\text{Now, Putting y = 16 in Equation (1) we get }\\\\4\cdot x-3\times 16=0\\\implies 4\cdot x=48\\\bf\implies x=12$

Hence the numbers are 12 and 16

So, the correct option is B. (12,16)