Question

The denominator of a rational number is greater than its numerator by 6. If the numerator is increased by 5 and the denominator is decreased by 3, the number obtained is equal to 5 4. Find the rational number.

Answer 1

let the numerator be x then, denominator be x-6
according to question,
x+5 / x-6-3 = 5/4
x+5/x-9 = 5/4
therefore it can be written as
4x + 20 = 5x - 45
20 + 45 = 5x - 4x
65 = x
so, numerator will be 65 and denominator will be x-6 or 65 - 6 = 59

Answer 2

┏─━─━─━─━∞◆∞━─━─━─━─┓ ✭✮ӇЄƦЄ ƖƧ ƳƠƲƦ ƛƝƧƜЄƦ✮✭

┗─━─━─━─━∞◆∞━─━─━─━─┛

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Let the numerator be x.

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Then, the denominator of the rational number = x+ 6

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It is given that the numerator is increased by 5 and the denominator decreased by 3.

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∴ The numerator of the new rational no. = x +5

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Denominator of the new rational no. = (x + 6)-3

= x + 3

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∴ New rational number = x + 5/ x + 3

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But the new rational number is given as 5/4.

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$\bf ∴ \frac{x + 5}{x + 3} = \frac{5}{4}$

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By cross multiplication, we get,

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$\bf \implies4(x + 5) = 5(x + 3)$

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$\bf \implies4x + 20 = 5x + 15$

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$\bf \implies4x - 5x = 15 - 20$

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$\bf \implies - x = - 5$

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$\bf \implies x = 5$

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∴ Numerator of the rational number = 5

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Denominator of the rational number = 5+6 = 11

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∴ Rational number = 5/11

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Verification :

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$\bf \frac{Original \: numerator + 5 }{Original \: Denominator -3} = \frac{5 + 5}{11 - 3}$

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$\bf \: \: \: \: \: = \frac{10}{8}$

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$\bf \: \: \: \: \: = \frac{5}{4}$

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$\huge\tt\purple {Hence \: Verified}$