Two numbers are in the ratio 3:5 .If 9 is subtracted from each,the new numbers are in the ratio 12:23. Find the smaller number.
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Answered by
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Answer:
Smaller number = 33
Bigger number = 55
Step-by-step explanation:
Let the numbers in the ratio 3 : 5 be 3x and 5x
If 9 subtracted from each of them, the numbers becomes 3x - 9 and 5x - 9
When 9 subtracted from 3x and 5x, the ratio of the numbers becomes 12 : 23.
According to the question,
\dfrac{3x - 9}{5x - 9} = \dfrac{12}{23}
23(3x - 9) = 12(5x - 9)
69x - 207 = 60x - 108
69x - 60x = 207 - 108
9x = 99
x = \dfrac{99}{9}
x = 11
Therefore,
Smaller number = 3x=3×11=33
Bigger number = 5x=5×11=55
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