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In a school there are two sections A and B. When a few students from

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In a school there are two sections A and B. When a few students from  [#permalink]

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New post 11 Nov 2019, 02:34
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C
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Question Stats:

44% (03:01) correct 56% (02:44) wrong based on 41 sessions

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In a school there are two sections A and B. When a few students from section B took transfer to section A the strength of section A increased by 22.5% and strength of B decreased by 30%. Now, what percentage of students in section A should be given a transfer to section B such that section A and section B have the same strengths?


A. \(\frac{100}{7}\)%

B. 20%

C. \(\frac{200}{7}\)%

D. 40%

E. \(\frac{300}{7}\)%



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Re: In a school there are two sections A and B. When a few students from  [#permalink]

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New post 11 Nov 2019, 03:11
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1
let students in class B = 100
after decrease = 70 ; so 30 were transfered
Section A = x
x+30 = 1.225x
x= ~ 133
new strength = 133+30 ; 163
to have equal strength 163-70 ; 93 ~ 46 students have to be tranfered to B
so 46/163 ; ~ 28%
IMO C


Bunuel wrote:
In a school there are two sections A and B. When a few students from section B took transfer to section A the strength of section A increased by 22.5% and strength of B decreased by 30%. Now, what percentage of students in section A should be given a transfer to section B such that section A and section B have the same strengths?


A. \(\frac{100}{7}\)%

B. 20%

C. \(\frac{200}{7}\)%

D. 40%

E. \(\frac{300}{7}\)%



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Re: In a school there are two sections A and B. When a few students from  [#permalink]

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New post 12 Nov 2019, 02:04
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Hi,
IMO C.

Let B had 100 students and 30 were transferred to A.
A’s new strength =A’ =1.225A
Change = 30 = 0.225A,
A= 400/3
A’ = 400/3 + 30 = 490/3
Let x students need to be transferred from A to B to get them equal.
490/3 - x = 70+x
x=140/3
In percentage of A = (140/3) / (490/3) = 28% = 200/7
C

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Re: In a school there are two sections A and B. When a few students from  [#permalink]

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New post 24 Nov 2019, 22:05

Solution


Given:
    • In a school there are two sections A and B.
    • When a few students from section B took transfer to section A the strength of section A increased by 22.5% and strength of B decreased by 30%

To find:
    • Now, what percentage of students in section A should be given a transfer to section B such that section A and section B have the same strengths

Approach and Working Out:
    • Let the strength of sections A and B be A and B respectively
    • If x students take transfer, then the new strengths will be A + x and B - x

Now, we are given that
    • A + x = 1.225A, and
    • B – x = 0.7B
    • Solving two equations, we get, \(A = \frac{4B}{3}\)
      o Implies, \(1.225A = \frac{49A}{40} = \frac{49B}{30}\), and
      o \(0.7B = \frac{7B}{10}\)

Again, if y students are transferred from the new strengths A to B then sections A and B will have equal strength
    • \(\frac{49B}{30} – y = \frac{7B}{10} + y\)
    o Implies, \(y = \frac{7B}{15}\)

Thus, percentage of students to be transferred = \(\frac{7B}{15}/\frac{49B}{30} = \frac{200}{7}%\)

Hence, the correct answer is Option C.

Answer: C
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Re: In a school there are two sections A and B. When a few students from  [#permalink]

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New post 07 Dec 2019, 04:27
It took some time for me to understand this. But here goes..

same no of students have been removed from B and added to A, yet different percentage, so find the relationship.

30% of B = 22.5% of A
which gives, A = (4/3)B

With this, now i can easily frame a number.. Say
A
400 -> 22.5% increase -> 490
B
300 -> 30% dec -> 210

Difference has to be divided by 2 ( since we want them to be the same ) so, 280/2 = 140.

140/490 = 0.28 hence a 28%
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Re: In a school there are two sections A and B. When a few students from   [#permalink] 07 Dec 2019, 04:27
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