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# A's present age in years is 40% of B's age. In X years, A's age will

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Joined: 02 Sep 2009
Posts: 64243
A's present age in years is 40% of B's age. In X years, A's age will  [#permalink]

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02 Apr 2020, 08:18
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25% (medium)

Question Stats:

92% (02:28) correct 8% (02:48) wrong based on 13 sessions

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A's present age in years is 40% of B's age. In X years, A's age will be half of B's age. By what percentage will B's age increase during these X years?

A. 5
B. 10
C. 15
D. 20
E. 25

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Re: A's present age in years is 40% of B's age. In X years, A's age will  [#permalink]

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02 Apr 2020, 08:36
A = 0.4B - (1)
A+x = (B+x)/2 - (2)
Put (1) in (2)
0.8B +2x = B + x
x = 0.2B
so in X years the increase is 0.2B i.e. 20%.

Bunuel wrote:
A's present age in years is 40% of B's age. In X years, A's age will be half of B's age. By what percentage will B's age increase during these X years?

A. 5
B. 10
C. 15
D. 20
E. 25
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Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
A's present age in years is 40% of B's age. In X years, A's age will  [#permalink]

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Updated on: 02 Apr 2020, 08:41
[quote="Bunuel"]A's present age in years is 40% of B's age. In X years, A's age will be half of B's age. By what percentage will B's age increase during these X years?

A. 5
B. 10
C. 15
D. 20
E. 25[/quote]

— A ———— B ———
— 0.4a ——— a ——— Present
— 0.4a+x —— a+x —— After x years

In X years, A's age will be half of B's age
—> 0.4a + x = 1/2(a + x)
—> 0.8a + 2x = a + x
—> x = 0.2a

% increase of B’s age = (x + a - a)/a*100
= x/a*100
= 0.2*100 = 20

Option D

[size=80][b][i]Posted from my mobile device[/i][/b][/size]

Originally posted by Dillesh4096 on 02 Apr 2020, 08:40.
Last edited by Dillesh4096 on 02 Apr 2020, 08:41, edited 1 time in total.
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Re: A's present age in years is 40% of B's age. In X years, A's age will  [#permalink]

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02 Apr 2020, 08:40
let, at present B's age is a
so, A's age is 0.4a
in X years , A's age will be half of B's age
so, a+x = 2*(0.4+x)
or, a=0.2x

in x years, B's age increase x
so, percentage of increase = (x/a)*100 = 0.2*100 = 20

Re: A's present age in years is 40% of B's age. In X years, A's age will   [#permalink] 02 Apr 2020, 08:40