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ICSE Class 9 Answered

When a two digit number is divided by the sum of its digits, the quotient is 7. If the ten's digit is diminished by twice the unit's digit, the remainder is zero. What is the number?
Asked by hemanginivyas92.9spicertl | 28 Jul, 2020, 05:14: PM
Expert Answer
Let the ten's and unit's digits be respectively x and y
As per the question, we have
10x+y=7(x+y)
10x+y=7x+7y
3x-6y=0
x-2y=0 ... (i)
And, x-2y=0 ...(ii)
This gives us two same equations and so we can't find the unique values for x and y.
The question should be:
When a two digit number is divided by the sum of its digits, the quotient is 8. If the ten's digit is diminished by thrice the unit's digit, the remainder is zero. What is the number?
Solution:
Taking x and y as the the ten's and unit's digits respectively, we have
2x - 7y = 0 ...(i)
And, x - 3y = 1 ... (ii)
Solving (i) and (ii), we get
x = 7 and y = 2
Hence, the required number is 72.
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