Question 12 of 49intermediate🔧 ApplyNumerical3 marks

The difference between two positive integers is 63. The ratio of the two integers is 2:5. Find the two integers.

Correct Answer

42 and 105

Exercise: Exercise Set 2.2 | Q: 4 | (Page 6)
For More Understanding

Explanation

The ratio of the two positive integers is given as 2:5, so we can represent them as 2x and 5x. The difference between these integers is given as 63. Setting up the equation 5x - 2x = 63 allows us to solve for x, which comes out to be 21. Substituting the value of x back into 2x and 5x gives the two integers as 42 and 105 respectively.

Solution Steps

  1. Step 1: Let the two positive integers be 2x and 5x since their ratio is 2:5.

  2. Step 2: According to the question, the difference between the two integers is 63. So, 5x - 2x = 63.

  3. Step 3: Simplify the equation to find the value of x: 3x = 63, which gives x = 21.

  4. Step 4: Substitute the value of x back to find the two integers. First integer = 2x = 2×212 \times 21 = 42. Second integer = 5x = 5×215 \times 21 = 105.

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