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# John and Mike had equal amount of money in savings at the beginning of

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Math Expert
Joined: 02 Sep 2009
Posts: 58335
John and Mike had equal amount of money in savings at the beginning of  [#permalink]

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14 Jul 2015, 01:00
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5% (low)

Question Stats:

94% (01:42) correct 6% (01:44) wrong based on 95 sessions

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John and Mike had equal amount of money in savings at the beginning of last year. Then Mike’s savings increased by 20% by the end of last year and decreased by 20% this year. John’s savings at first decreased by 20% by the end of last year and then increased by 20% this year. What percentage of John’s and Mike’s savings combined are John’s savings alone?

A. 25%
B. 40%
C. 50%
D. 75%
E. 96%

Kudos for a correct solution.

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Re: John and Mike had equal amount of money in savings at the beginning of  [#permalink]

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14 Jul 2015, 02:49
2
Bunuel wrote:
John and Mike had equal amount of money in savings at the beginning of last year. Then Mike’s savings increased by 20% by the end of last year and decreased by 20% this year. John’s savings at first decreased by 20% by the end of last year and then increased by 20% this year. What percentage of John’s and Mike’s savings combined are John’s savings alone?

A. 25%
B. 40%
C. 50%
D. 75%
E. 96%

Kudos for a correct solution.

Solution -
Amount of money in savings at the beginning of last year = X
Mikes savings this year = 1.2*0.8*X = 0.96X -----------------1
Johns savings this year = 0.8*1.2*X = 0.96X -----------------2
2/(1+2) 1.e., Percentage of John’s and Mike’s savings combined are John’s savings alone = 0.96X/(0.96X+0.96X) *100 = 1/2*100 = 50%
ANS C
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Re: John and Mike had equal amount of money in savings at the beginning of  [#permalink]

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14 Jul 2015, 04:29
Bunuel wrote:
John and Mike had equal amount of money in savings at the beginning of last year. Then Mike’s savings increased by 20% by the end of last year and decreased by 20% this year. John’s savings at first decreased by 20% by the end of last year and then increased by 20% this year. What percentage of John’s and Mike’s savings combined are John’s savings alone?

A. 25%
B. 40%
C. 50%
D. 75%
E. 96%

Kudos for a correct solution.

Percentage question calls for using the total amount of JOhna nd Mike be 100 \$

For John ----> 100 * 0.8 * 1.2 ----> 96 \$ (as there was a 20% decrease followed by a 20% increase)

For Mike ---> 100*1.2*0.8 ----> 96\$ (as there was a 20% increase followed by a 20% decrease)

Thus % of JOhn's savings = 96 / (96+96) = 50%. Thus C is the correct answer.
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John and Mike had equal amount of money in savings at the beginning of  [#permalink]

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14 Jul 2015, 05:25
Bunuel wrote:
John and Mike had equal amount of money in savings at the beginning of last year. Then Mike’s savings increased by 20% by the end of last year and decreased by 20% this year. John’s savings at first decreased by 20% by the end of last year and then increased by 20% this year. What percentage of John’s and Mike’s savings combined are John’s savings alone?

A. 25%
B. 40%
C. 50%
D. 75%
E. 96%

Kudos for a correct solution.

Let, Mike's Saving at the beginning of last year = 100
i.e. John's Saving at the beginning of last year = 100

Now, Mike's Saving at the End of last year = 120 [after 20% increase]
and Mike's Saving This year = 120 - 20% of 120 = 120 - 24 = 96 [after 20% Decrease]

Now, John's Saving at the End of last year = 100 - 20% of 100 = 100-20 = 80 [after 20% Decrease]
and John's Saving This year = 80 + 20% of 80 = 80+16 = 96 [after 20% increase]

Combined Savings of John and Mike = 96+96 = 192

John’s savings alone as percentage of John’s and Mike’s combined savings = (96/192)*100 = 50%

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Re: John and Mike had equal amount of money in savings at the beginning of  [#permalink]

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14 Jul 2015, 07:05
Bunuel wrote:
John and Mike had equal amount of money in savings at the beginning of last year. Then Mike’s savings increased by 20% by the end of last year and decreased by 20% this year. John’s savings at first decreased by 20% by the end of last year and then increased by 20% this year. What percentage of John’s and Mike’s savings combined are John’s savings alone?

A. 25%
B. 40%
C. 50%
D. 75%
E. 96%

Kudos for a correct solution.

John: (-20%) --- (+20%) = 100 - 20 + 16 = 96
Mike: (+20%) --- (-20%) = 100 + 20 - 24 = 96

So, John's savings is 50% of their combined savings. Ans (C).
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Re: John and Mike had equal amount of money in savings at the beginning of  [#permalink]

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17 Jul 2015, 02:32
Consider Savings as 100 so
Mike -> 100 *1.2 * 0.8 = 96
John -> 100 * 0.8 * 1.2 = 96

So, 50%
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Joined: 20 Jul 2011
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Re: John and Mike had equal amount of money in savings at the beginning of  [#permalink]

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18 Jul 2015, 05:44
Bunuel wrote:
John and Mike had equal amount of money in savings at the beginning of last year. Then Mike’s savings increased by 20% by the end of last year and decreased by 20% this year. John’s savings at first decreased by 20% by the end of last year and then increased by 20% this year. What percentage of John’s and Mike’s savings combined are John’s savings alone?

A. 25%
B. 40%
C. 50%
D. 75%
E. 96%

Kudos for a correct solution.

Assume John and Mike had 100 rs. at the beginning of last year.

John = 100 * 120/100 * 80/100 = 96
Mike = 100 * 80/100 * 120/100 = 96

Combined Savings = 192
John's savings as % of combined savings = 96/192 * 100 = 50%

Option C
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Posts: 7940
Re: John and Mike had equal amount of money in savings at the beginning of  [#permalink]

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18 Jul 2015, 05:54
1
Bunuel wrote:
John and Mike had equal amount of money in savings at the beginning of last year. Then Mike’s savings increased by 20% by the end of last year and decreased by 20% this year. John’s savings at first decreased by 20% by the end of last year and then increased by 20% this year. What percentage of John’s and Mike’s savings combined are John’s savings alone?

A. 25%
B. 40%
C. 50%
D. 75%
E. 96%

Kudos for a correct solution.

mikes savings= 1.2x*.8
johns savings=.8x*1.2
therefore the savings are same for both..
each's is 50% of total
ans C
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Posts: 58335
Re: John and Mike had equal amount of money in savings at the beginning of  [#permalink]

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19 Jul 2015, 13:20
Bunuel wrote:
John and Mike had equal amount of money in savings at the beginning of last year. Then Mike’s savings increased by 20% by the end of last year and decreased by 20% this year. John’s savings at first decreased by 20% by the end of last year and then increased by 20% this year. What percentage of John’s and Mike’s savings combined are John’s savings alone?

A. 25%
B. 40%
C. 50%
D. 75%
E. 96%

Kudos for a correct solution.

800score Official Solution:

Let’s denote by x amount of money each of them had in savings at the beginning of last year.

Considering changes in Mike’s savings he currently has 1.2 × 0.8 × x = 0.96x
Considering changes in John’s savings he currently has 0.8 × 1.2 × x = 0.96x

In order to calculate what percentage of John’s and Mike’s savings combined are John’s savings alone we divide Jon’s savings alone by John’s and Mike’s savings combined:
0.96x / (0.96x + 0.96 x) = 1/2 =0.5 = 50%.

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Re: John and Mike had equal amount of money in savings at the beginning of  [#permalink]

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16 Dec 2018, 19:53
Considering Mike's savings as 100, at the end of first year with 20% increase would be 120 and at the end of second year with 20% decrease from 120 would be equal to (120-(12+12)) = 96
Similarly, having John's savings to be 100, at the end of first year it would be 80 and at the end of second year with 20% increase from 80 would be equal to (80+(8+8)) = 96

Calculating the percentage of John's savings to total savings is [96/(96*2)]*100 = 50% (Option C)
Re: John and Mike had equal amount of money in savings at the beginning of   [#permalink] 16 Dec 2018, 19:53
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