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UPSC NDA 2 2017 Mathematics Solved Paper
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© examsnet.com
Question : 20
Total: 120
A person is to count 4500 notes. Let an denote the number of notes he counts in the nth minute. If
a
1
=
a
2
=
a
3
=
.
.
=
a
10
=
150
, and
a
10
,
a
11
,
a
12.
.
.
are in AP with the common difference −2 , then the time taken by him to count all the notes is
[NDA II 2017]
24 minutes
34 minutes
125 minutes
135 minutes
Validate
Solution:
Let us assume that total minutes
=
x
For first nine minutes
=
150
×
9
Let the remaining minutes
=
y
=
x
−
9
Now,
(
150
×
9
)
+
y
2
[
2
×
150
+
(
y
−
1
)
(
−
2
)
]
=
4500
y
2
(
302
−
2
y
)
=
3150
⇒
y
2
−
151
y
+
3150
=
0
⇒
(
y
−
126
)
(
y
−
25
)
=
0
⇒
y
=
25
or
126
(Rejected)
So,
x
=
y
+
9
=
25
+
9
=
34
minutes
© examsnet.com
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