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प्रश्न
Two consecutive natural numbers are such that one-fourth of the smaller exceeds one-fifth of the greater by 1. Find the numbers.
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उत्तर
Let two consecutive natural numbers = x, x+1
∴ One-fourth of the smaller = `"x"/4`
one-fifth of the greater = `("x" + 1)/5`
According to the statement:
`"x"/4 = ("x" + 1)/5 + 1 => "x"/4 - ("x" + 1)/5 = 1`
`=> (5"x" - 4("x" + 1))/20 = 1 => (5"x" - 4"x" - 4)/20 = 1`
`=> ("x" - 4)/20 = 1`
⇒ x - 4 = 20 ...(Cross multiplying)
⇒ x = 20 + 4 ⇒ x = 24
∴ x + 1 = 24 + 1 = 25
Two consecutive numbers are 24 and 25
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