1) The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the rational number.
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1) The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the rational number.
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Answer:
Explanation:
Given that,
So,
Let numerator be 'x' and denominator be 'y'
Then,
→ y = x + 8 ....equation(1)
Also given that,
so,
→ (x + 17)/(y - 1) = 3/2
[cross multiplying]
→ 2x + 34 = 3y - 3
→ 2x - 3y = -37
[Using equation(1)]
→ 2x - 3(x + 8) = -37
→ 2x - 3x -24 = -37
→ -x = -13
→ x = 13
Putting value of x in equation (1)
→ y = x + 8
→ y = 13 + 8
→ y = 21
Therefore,
The required rational number will be, x/y = 13/21.
Answer:
Given :-
To Find :-
Solution :-
Let, the numerator be x
And, the denominator will be x + 8
Then, the number is
According to the question,
⇒
⇒
By doing cross multiplication we get,
⇒
⇒
⇒
➠
Hence, the required rational number are,
↦
↦
➦
The rational number is .
Let's Verify :-
⇒
⇒
Put x = 13 we get,
⇒
⇒
⇒
⇒
➦ LHS= RHS
➲ Hence, Verified ✔