Question
Download Solution PDFThe present ages of two cousins is in the ratio of 3 : 4. After 4 years, their ages are in the ratio of 10 : 13. The ratio of the ages of the two cousins after 6 years is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Present age ratio = 3 : 4
Age ratio after 4 years = 10 : 13
Calculation:
Let the present ages of the two cousins be 3x and 4x years respectively.
After 4 years, their ages will be (3x + 4) and (4x + 4) years respectively.
According to the question:
⇒ (3x + 4) / (4x + 4) = 10 / 13
⇒ 13(3x + 4) = 10(4x + 4)
⇒ 39x + 52 = 40x + 40
⇒ 52 - 40 = 40x - 39x
⇒ 12 = x
Present ages are:
First cousin = 3x = 3 × 12 = 36 years
Second cousin = 4x = 4 × 12 = 48 years
Ages after 6 years:
First cousin = 36 + 6 = 42 years
Second cousin = 48 + 6 = 54 years
Ratio of their ages after 6 years = 42 : 54 ⇒ 7 : 9
The ratio of the ages of the two cousins after 6 years is 7 : 9.
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