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

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Math Expert
Joined: 02 Sep 2009
Posts: 59721
In a school there are two sections A and B. When a few students from  [#permalink]

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11 Nov 2019, 02:34
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Difficulty:

95% (hard)

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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11 Nov 2019, 03:11
2
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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Joined: 19 Sep 2017
Posts: 230
Location: United Kingdom
GPA: 3.9
WE: Account Management (Other)
Re: In a school there are two sections A and B. When a few students from  [#permalink]

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12 Nov 2019, 02:04
1
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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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.

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Joined: 21 Apr 2019
Posts: 33
Re: In a school there are two sections A and B. When a few students from  [#permalink]

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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%
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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