Question
Download Solution PDFTwo numbers are in the ratio of 5 ∶ 7. If 6 be added to each, the ratio becomes 3 ∶ 4. Find the numbers.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Ratio of two numbers = 5 : 7
When 6 is added to each, new ratio = 3 : 4
Calculation:
Let the numbers be 5x and 7x.
According to the question,
⇒ \(\frac{5x+6}{7x+6}=\frac{3}{4}\)
⇒ 4(5x + 6) = 3(7x + 6)
⇒ 20x + 24 = 21x + 18
⇒ 21x – 20x = 24 – 18
⇒ x = 6
First number = 5x = 5 × 6 = 30
Second number = 7x = 7 × 6 = 42
Therefore, the two numbers are 30 and 42.
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