Two numbers are in the ratio 7 : 8. When 5 is subtracted from both numbers, their ratio becomes 2 : 3. Find the numbers.
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Two numbers are in the ratio 7 : 8. When 5 is subtracted from both numbers, their ratio becomes 2 : 3. Find the numbers.
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Answer:
This is the correct answer
ᴀɴsᴡᴇᴇ
we have,
let the numbers are 7x and 8x
and according to the question
( when 5 is subtracted from both numbers, their ratio becomes 2:3)
[tex] \bold{ : \implies \frac{7x - 5}{8x - 5} = \frac{2}{3} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ : \implies3(7x - 5) = 2(8x - 5) \: } \: \: \: \\ \\ \bold{ : \implies 21x - 15 = 16x - 10 } \: \: \: \: \: \: \\ \\ \bold{: \implies21x - 16x = - 10 + 15} \: \: \\ \\ \bold{ : \implies5x = 5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ : \implies \: x = \cancel{ \frac{5}{5}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ : \implies \boxed{ \bold{x = 1}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
so, x = 1 is common multiple of numbers
then,numbers are
so, numbers are 7 and 8