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

Question

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.

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

Kudos for a correct  solution .

balamoon · Answer

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

ENGRTOMBA2018 · Answer

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.

GMATinsight · Answer

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  
and Mike's Saving This year = 120 - 20% of 120 = 120 - 24 = 96

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

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%

Answer: Option C

TimeTraveller · Answer

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).

sanket1991 · Answer

Consider Savings as 100 so 
Mike -> 100 *1.2 * 0.8 = 96
John -> 100 * 0.8 * 1.2 = 96

So, 50%

ashokk138 · Answer

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

chetan2u · Answer

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

Bunuel · Answer

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%.

The answer is C.

Chandru22 · Answer

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  *100 = 50% (Option C)

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

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