the denominator of a rational number is greater than its numerator by 7 if the numerator is increased by 17 and the denominator is decreased by 6 the new number become 12 find the original number
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120
Answer -
Original number is 5/82
Explanation -
Let the numerator be N and denominator be D.
The denominator of a rational number is greater than its numerator by 7.
If we add 7 to numerator then, both numerator and denominator becomes equal.
i.e.
...(1)
If the numerator is increased by 17 and the denominator is decreased by 6 the new number become 12.
Now,
- Numerator = N + 17
- Denominator = D - 6
Fraction of both numerator (N + 17) and denominatior (D - 6) is equal to a number i.e. 12.
We can also, write it like -
Cross-multiply them
...(2)
Substitute value of (1) in (2)
Substitute value of N in (1)
Now,
•°• Original number is 5/82.
Verification -
From the above calculations we have -
- Numerator = N = 5/11
- Denominator = D = 82/11
Substitute value of N and D in equation (1)
=>
=>
=>
Similarly, substitute value of N and D in equation (2)
=>
=>
=>
=>
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