Question
Download Solution PDFTwo numbers are in the ratio 7 : 11. On adding 7 to each of these, their ratio becomes 2 : 3. Which of these is. the smaller number?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Two numbers are in the ratio 7:11.
On adding 7 to each, their ratio becomes 2:3.
Formula used:
If two numbers are in the ratio a:b, the numbers can be written as 7x and 11x.
After adding a constant, their new ratio becomes (7x + constant):(11x + constant).
Given new ratio = 2:3.
Calculation:
New ratio (7x + 7):(11x + 7) = 2:3
⇒ (7x + 7)/(11x + 7) = 2/3
⇒ 3 × (7x + 7) = 2 × (11x + 7)
⇒ 21x + 21 = 22x + 14
⇒ 22x - 21x = 21 - 14
⇒ x = 7
Smaller number = 7x = 7 × 7 = 49
∴ The correct answer is option (2).
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