Question

(1) What same number should be added to 2, 5, 10 and 19 so that the resulting numbers are proportional?​

Answer 1

• Let x be added to 5, 11, 19 and 37 to make them in proportion.

5 + x : 11 + x : : 19 + x : 37 + x

• (5 + x) (37 + x) = (11 + x) (19 + x)

→ 185 + 5x + 37x + x² = 209 + 11x + 19x+x2

→ 185 +42x + x² = 209 + 30x + x²

→ 185 +42x + x² = 209 + 30x + x²42x - 30x + x² - x² = 209 - 185

→ 185 +42x + x² = 209 + 30x + x²42x - 30x + x² - x² = 209 - 185⇒ 12x = 24

→ 185 +42x + x² = 209 + 30x + x²42x - 30x + x² - x² = 209 - 185⇒ 12x = 24⇒ x = 2

.. Least number to be added = 2.

Answer 2

SOLUTiON

Let assume the number be x

⠀⠀⠀⠀⠀⠀⠀⠀⠀ATQ

• (3+x) : (5+x) = (13+x) : (19+x)
• (3+x) × (19+x) = (5+x) × (13+x)
• 57 + 22x + x² = 65 + 18x + x²
• 22x−18x+x²−x² = 65–57
• 4x=8
• x=2

VERiFiCATiON

• 3+2 = 5
• 5+2 = 7
• 13+2 = 15
• 19+2 = 21

15/21 = 5/7

★ Thus, The answer is 2

▬▭▬▭▬▭▬▭▬▭▬▭▬▭▬▭▬▭▬▭▬