The difference between two number is 3 and the difference of their squ

1.	The difference between two number is 3 and the difference of their square is 69. Find the numbers1. 13 and 102. 10 and 73. 13 and 74. 12 and 15
Answer» Correct Answer - Option 1 : 13 and 10 Given The difference between two number = 3 Difference of their square = 69 Calculation Let the greater number = x ⇒ Smaller number = x - 3 From question ⇒ x² - (x - 3)² = 69 ⇒ x² - (x² - 2 × 3 × x + 3²) = 69 ⇒ x² - x² + 6x - 9 = 69 ⇒ 6x - 9 = 69 ⇒ 6x = 69 + 9 ⇒ 6x = 78 ⇒ x =(78/6) ⇒ x = 13 ⇒ Greater number = 13 and ⇒ Smaller number = 13 - 3 ⇒ Smaller number = 10 ∴ Greater number = 13 and smaller number = 10 Alternate method Let small number = x ⇒ Greater number = x + 3 From question ⇒ (x + 3)² - x² = 69 ⇒ (x² + 2 × x × 3 + 3²) - x² = 69 ⇒ (x² + 6x + 9) - x² = 69 ⇒ x² + 6x + 9 - x² = 69 ⇒ 6x + 9 = 69 ⇒ 6x = 69 - 9 ⇒ 6x = 60 ⇒ x = (60/6) ⇒ x = 10 ⇒ Greater number = 10 + 3 ⇒ Greater number = 13 ∴ Greater number = 13 and smaller number = 10

The difference between two number is 3 and the difference of their square is 69. Find the numbers1. 13 and 102. 10 and 73. 13 and 74. 12 and 15

Answer» Correct Answer - Option 1 : 13 and 10

Given

The difference between two number = 3

Difference of their square = 69

Calculation

Let the greater number = x

⇒ Smaller number = x - 3

From question

⇒ x² - (x - 3)² = 69

⇒ x² - (x² - 2 × 3 × x + 3²) = 69

⇒ x² - x² + 6x - 9 = 69

⇒ 6x - 9 = 69

⇒ 6x = 69 + 9

⇒ 6x = 78

⇒ x =(78/6)

⇒ x = 13

⇒ Greater number = 13 and

⇒ Smaller number = 13 - 3

⇒ Smaller number = 10

∴ Greater number = 13 and smaller number = 10

Alternate method

Let small number = x

⇒ Greater number = x + 3

From question

⇒ (x + 3)² - x² = 69

⇒ (x² + 2 × x × 3 + 3²) - x² = 69

⇒ (x² + 6x + 9) - x² = 69

⇒ x² + 6x + 9 - x² = 69

⇒ 6x + 9 = 69

⇒ 6x = 69 - 9

⇒ 6x = 60

⇒ x = (60/6)

⇒ x = 10

⇒ Greater number = 10 + 3

⇒ Greater number = 13

∴ Greater number = 13 and smaller number = 10