Question

Two numbers are in the ratio of 2:3. The total sum of the numbers is 75. Then find the numbers.

Answer 1

$\sf \: Let \: common \: factor \: be \: x.$

$\Rrightarrow \sf 2x + 3x = 75 \\ \Rrightarrow \sf 5x = 75 \\ \Rrightarrow \sf x = \frac{ { \cancel{75}}^{ \: 15} }{ { \cancel{5}}^{ \: 1} } \\ \boxed{ \sf \: x = 15}$

$\sf \: Now \: the \: numbers \: are \hookrightarrow$

$\rightarrow \sf \: 2x = 2(15) = 30\\ \rightarrow \sf \: 3x = 3(15) = 45$

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Answer 2

Answer

• The numbers are 30 and 45.

Step-by-step explanation:

Given :-

• Two numbers are in the ratio of 2 : 3. The total sum of the numbers is 75.

To Find :-

• What are the numbers.

Solution :-

➊ To find the numbers, firstly let us consider the two numbers be 2x and 3x.

Given :

• Sum of the numbers = 75.
• Numbers = 2x and 3x.

According to the question,

↦ 2x + 3x = 75

↦ 5x = 75

↦ x = 75/5

➦ x = 15

➋ Now, let us find out the numbers by putting the value of x in the assumed numbers.

➲ First number = 2x = 2 × 15 = 30.

➲ Second number = 3x = 3 × 15 = 45.

∴ Hence, the numbers are 30 and 45.

❖ Verification ❖

↦ 2x + 3x = 75

Putting x = 15 we get,

↦ 2(15) + 3(15) = 75

↦ 2 × 15 + 3 × 15 = 75

↦ 30 + 45 = 75

↦ 75 = 75

➦ LHS = RHS

∴ Hence, Verified ✔