The denominator of a rational number is twice its numerator .if the numerator is decreased by 2 and denominator increased by 4 the no obtained is 3/7 find the rational number
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Answer:-
Let the number be x/y.
Given:
The denominator is twice the numerator.
→ y = 2x -- equation (1)
And,
If the numerator is decreased by 2 and denominator is increased by 4 the number obtained is 3/7
→ (x - 2)/(y + 4) = 3/7
On cross multiplication we get,
→ 7(x - 2) = 3(y + 4)
→ 7x - 14 = 3y + 12
Substitute y value from equation (1).
→ 7x - 14 = 3(2x) + 12
→ 7x - 14 = 6x + 12
→ 7x - 6x = 12 + 14
→ x = 26
Substitute x value in equation (1)
→ y = 2(26)
→ y = 52
Hence, the rational number is 26/52 (1/2).
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