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  • Two numbers are in the ratio 5ratio 6. If 8 is subtracted from each of the numbers, the ratio becomes 4ratio5. Find the numbers

Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers, the ratio becomes 4:5. Find the numbers

Answers (1)

Solution:
Let x and y be two numbers
According to question
x : y = 5 : 6
\frac{x}{y}= \frac{5}{6}
x = \frac{5y}{6}            … (1)
According to second condition

\frac{x-8}{y-8}= \frac{4}{5}
5x – 40 = 4y – 32
5x – 4y = –32 + 40
5x – 4y = 8      … (2)
Put value of x from equation (1) in (2) we get

5\left ( \frac{5y}{6} \right )-4y= 8

\frac{25y}{6}-4y= 8

\frac{25y-24y}{6}= 8
25y – 24y = 48
y = 48
Put y = 48 in eq. (1)
x = \frac{5\times 48}{6}
x = 40

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