16. A two-digit number is such that the product of its digits is 35. If 18
is added to the number, the digits interchange their places. Find the
number.
17. A two-digit number is such that the product of its digits is 18. When 63
is subtracted from the number, the digits interchange their places. Find
the number.
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Answers
Answer:
16.Answer: Numbers are 57 and 75.
Step-by-step explanation:
Let the unit digit be 'x'
Let the ten's digit be 'y'.
Original number will be
\begin{lgathered}10\times \text{ten's digit}+one's\ digit\\\\=10x+y\end{lgathered}
10×ten’s digit+one
′
s digit
=10x+y
On interchanging of digits,
Let unit's digit be 'y'.
Let ten's digit be 'x'.
New number will be
\begin{lgathered}10\times \text{ten's digit}+one's\ digit\\\\=10y+x\end{lgathered}
10×ten’s digit+one
′
s digit
=10y+x
According to question,
Product of digit of two digit number = 35
So, it becomes,
xy=35-----------(1)xy=35−−−−−−−−−−−(1)
If we add 18 to the number the new number obtained is number formed by interchange of digits.
17.
Answer:
Let the two - digit number be xy (i.e. 10x + y).
After reversing the digits of the number xy, the new number becomes yx (i.e. 10y + x).
According to question -
xy = 18
⇒ x = 18/y.....(1)
and,
(10x + y) - 63 = (10y + x)
⇒ 9x - 9y = 63
⇒ x - y = 7.....(2)
Substituting the value of x in equation (2), we get -
⇒ 18 - y2 = 7y
⇒ y2 + 7y - 18 = 0
⇒ y2 + 9y - 2y - 18 = 0
⇒ y(y + 9) - 2(y + 9) = 0
⇒ (y + 9)(y - 2) = 0
∴ y = 2
[y = - 9 is invalid because digits of a number cannot be negative.]
Substituting the value of y in equation (1), we get -
x = 9
Thus, the required number is 92.
Answer:
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