Question
Download Solution PDFThe ages of Misha and Kamal are in the ratio of 4 : 3 respectively. After 9 years the ratio of their ages will be 7 : 6. What is the difference in their present ages?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Ratio of Misha's age to Kamal's age (present) = 4 : 3
Ratio of their ages after 9 years = 7 : 6
Calculations:
Let Misha's present age be 4x years.
Let Kamal's present age be 3x years.
After 9 years:
Misha's age will be (4x + 9) years.
Kamal's age will be (3x + 9) years.
According to the given ratio after 9 years:
Cross-multiply the terms:
⇒ 6 × (4x + 9) = 7 × (3x + 9)
⇒ 24x + 54 = 21x + 63
⇒ 24x - 21x = 63 - 54
⇒ 3x = 9
⇒ x =
⇒ x = 3
Now, calculate their present ages:
Misha's present age = 4x = 4 × 3 = 12 years
Kamal's present age = 3x = 3 × 3 = 9 years
Difference in their present ages = Misha's present age - Kamal's present age
⇒ Difference = 12 - 9
⇒ Difference = 3 years
∴ The difference in their present ages is 3 years.
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