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CAT 2017 Quantitative Ability
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© examsnet.com
Question : 32
Total: 34
In the Garbar Jhala, Aminabad a shopkeeper first raises the price of a Jewellery by x% then he decreases the new price by x%. After one such up down cycle, the price of a Jewellery decreased by ₹ 21025. After a second up down cycle the jewellery was sold for ₹ 484416. What was the original price of the jewellery.
₹ 500000
₹ 600625
₹ 525625
₹ 526000
Validate
Solution:
Let the original price P, then the decrease in value of P afterone cycle
=
p
(
x
100
)
2
=
21025
Again the final value after second cycle
P
(
1
+
x
100
)
(
1
−
x
100
)
(
1
+
x
100
)
(
1
−
x
100
)
=
484416
P
[
1
−
(
x
100
)
2
]
=
484416
Dividing Eq. (ii) by Eq (i), we get
[
1
−
(
x
100
)
2
]
2
(
x
100
)
2
=
484416
21025
=
2304
100
1
−
(
x
100
)
2
(
x
100
)
2
=
√
2304
100
=
48
10
Let
x
100
=
k
,
then
1
−
k
2
k
=
48
10
10
k
2
+
48
k
−
10
=
0
5
k
2
−
24
x
−
5
=
0
k
=
5
or
k
=
−
1
5
So
x
=
20
%
Hence,
P
(
x
100
)
2
=
21025
P
=
525625
© examsnet.com
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