Question

$\huge\underline{\bf \orange{Question :}}$

The difference between two Numbers is 30. On dividing the greater by the smaller, the quotient is 3. find the numbers ​

Answer 1

Given :

• The difference between two Numbers = 30.
• On dividing the greater by the smaller, the quotient = 3.

To Find :

• These two numbers.

Solution :

Let, the greater number be x and smaller number be y .

According to the question –

• x - y = 30 ––––– (1)
• x/y = 3 –––––– (2)

From eqⁿ (1),

⪼ x - y = 30

⪼ x = 30 + y

Putting this value of x in eqⁿ (2),

⪼ (30 + y)/y = 3

⪼ 30 + y = 3y

⪼ 30 = 3y - y

⪼ 30 = 2y

⪼ y = 30/2

⪼ y = 15

Putting the value of y in eqⁿ (1),

⪼ x - y = 30

⪼ x - 15 = 30

⪼ x = 30 + 15

⪼ x = 45

Hence, the numbers are 15 and 45 .

Answer 2

Given :-

• The difference between two Numbers is 30
• On dividing the greater by the smaller, the quotient is 3

To Find :-

• The numbers

Solution :-

Let,

• The greater number be ‘x’
• The smaller number be ‘y’

A.T.Q :-

★ The difference between two Numbers is 30.

So,

$\to\sf x - y = 30 --- - (1)$

★ On dividing the greater by the smaller, the quotient is 3.

So,

$\to\sf \frac{x}{y} = 3 ---- (2)$

From equation (1) we get,

$:\implies\sf x - y = 30$

$:\implies\sf x = \boxed{\green{\sf30 + y}}$

Substituting the value of x in equation (2),

$:\implies\sf\frac{30 + y}{y} = 3$

$:\implies\sf 30 + y = 3y$

$:\implies\sf - 3y + y = - 30$

$:\implies\sf \cancel- 2y = \cancel- 30$

$:\implies\sf y = \frac{\cancel{30}}{\cancel2}$

$:\implies\sf\underline{\boxed{\blue{\sf y = 15}}}$

Substituting the value of y in equation (2),

$:\implies\sf\frac{x}{15} = 3$

$:\implies\sf x = 3 \times 15$

$:\implies\sf \underline{\boxed{\blue{\sf x = 45}}}$

Hence, the greater number is 45 and the smaller number is 15.