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UPSC CDS Math Number System Questions
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© examsnet.com
Question : 30
Total: 102
The age of a woman is a two-digit integer. On reversing this integer, the new integer is the age of her husband who is elder to her. The difference between their ages is one-eleventh of their sum. What is the difference between their ages ?
[2018 CDS-I]
8 years
9 years
10 years
11 years
Validate
Solution:
Let unit and tens digit of age of woman be y and x, respectively.
Age of woman
=
x
y
=
10
x
+
y
Age of husband
=
y
x
=
10
y
+
x
Now,
10
y
+
x
−
(
10
x
+
y
)
=
1
11
(
10
x
+
y
+
10
y
+
x
)
(
∵
y
x
>
x
y
)
⇒
9
y
−
9
x
=
x
+
y
⇒
8
y
=
10
x
⇒
x
y
=
4
5
So, age of woman = 45, age of husband = 54 years
Difference between their ages
=
54
–
45
=
9
years
© examsnet.com
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