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Math Expert V
Joined: 02 Sep 2009
Posts: 60647
Some people form a joint account for one year with the condition that  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 38% (03:27) correct 63% (02:22) wrong based on 16 sessions

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Some people form a joint account for one year with the condition that every month each member deposits an amount equal to the number of members in the account in that month. Also, the person who withdraws from the account before the end of the year get his/her amount at the end of the year. After 6 months, 1/4th of the people withdraw and 1/3rd of the remaining withdraw after 3 months. At the end of the year there is an amount of Rs. 4860 in the account before paying of the withdrawn amounts. Find out the number of people in the beginning of the year.

A. 12
B. 24
C. 36
D. 48
E. 60

Are You Up For the Challenge: 700 Level Questions

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Math Expert V
Joined: 02 Aug 2009
Posts: 8336
Re: Some people form a joint account for one year with the condition that  [#permalink]

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Bunuel wrote:
Some people form a joint account for one year with the condition that every month each member deposits an amount equal to the number of members in the account in that month. Also, the person who withdraws from the account before the end of the year get his/her amount at the end of the year. After 6 months, 1/4th of the people withdraw and 1/3rd of the remaining withdraw after 3 months. At the end of the year there is an amount of Rs. 4860 in the account before paying of the withdrawn amounts. Find out the number of people in the beginning of the year.

A. 12
B. 24
C. 36
D. 48
E. 60

Are You Up For the Challenge: 700 Level Questions

Let there be x members in the beginning..
So the duration can be divided in 3 parts..
(I) First 6 months -- number is x, so money per month = x*x, and for 6 months = $$6*x^2$$
(II) Next 3 months -- number reduces to $$\frac{3x}{4}$$, so money per month = $$(\frac{3x}{4})^2$$, and for 3 months = $$3*(\frac{3x}{4})^2=\frac{27x^2}{16}$$
(III) Last 3 months -- number reduces to $$\frac{3x}{4}*\frac{2}{3}=\frac{x}{2}$$, so money per month = $$(\frac{x}{2})^2$$, and for 3 months = $$3*(\frac{x}{2})^2=\frac{3x^2}{4}$$

Total = $$6x^2+\frac{27x^2}{16}+\frac{3x^2}{4}=4860........\frac{135x^2}{16}=4860........x^2=4860*\frac{16}{135}=36*16.....x=6*4=24$$

B
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Math Expert V
Joined: 02 Aug 2009
Posts: 8336
Re: Some people form a joint account for one year with the condition that  [#permalink]

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Bunuel wrote:
Some people form a joint account for one year with the condition that every month each member deposits an amount equal to the number of members in the account in that month. Also, the person who withdraws from the account before the end of the year get his/her amount at the end of the year. After 6 months, 1/4th of the people withdraw and 1/3rd of the remaining withdraw after 3 months. At the end of the year there is an amount of Rs. 4860 in the account before paying of the withdrawn amounts. Find out the number of people in the beginning of the year.

A. 12
B. 24
C. 36
D. 48
E. 60

Are You Up For the Challenge: 700 Level Questions

You can also make use of choices..

A. 12...
First 6 months = $$6*12*12$$.... next 3 months=$$3*(12*\frac{3}{4})^2=3*9*9$$...last 3 months = $$3*(9*\frac{2}{3})^2=3*6*6$$..
Total = $$864+243+108=1215\neq{4860}$$

B. 24...
First 6 months = $$6*24*24$$.... next 3 months=$$3*(24*\frac{3}{4})^2=3*18*18$$...last 3 months = $$3*(18*\frac{2}{3})^2=3*12*12$$..
Total = $$4860$$..
Also a quick look at choice A .. A is 12 and B is 2 times and we are dealing with x^2 only and in each term, so our answer here will be (2x)^2= 4* value for x = 4*1215=4860

No need to go furhter

B
_________________ Re: Some people form a joint account for one year with the condition that   [#permalink] 07 Nov 2019, 21:07
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