percents

[divya23]

in may lee earnings were 60% of the lee family's total income
in june lee eraned 20% more than in may
if the rest of the family income were same in both the months
then in june lee income was approx what % of lee family total income...
please explain this by taking values rather assuming the incomes as x...

ans = 64%

[winniethepooh]

Correct Ans is 64.29 rounded off to 64.

Let total family income be 100.
Therefore, Lee's income will be 60 and rest of the family income is 40.

Next month Lee's income increases by 20%, that is 20% of 60 = 12. Therefore Lee's total income is 60 + 12= 72.
Family's income is unchanged, that is 40.

So, Lee's Income is 72/112(72 + 40) x 100 = 64.29%, that is 64% of family income.

[winniethepooh]

To avoid confusion, if any (72 + 40) in last line of the previous reply is the total income break up of Lee's family and not included in the calculation of Lee's income % in family income.

[divya23]

damn!!!!!!!!! i made total income of the family as 100..dats y i was geting the rong ans....

[Roy@MasterGmat]

One of the trickier parts here is the final calculation, which is converting 72/112 into percents.

The direct approach of 72/112 * 100 might prove difficult for most, but reducing the fraction as much as possible before multiplying by 100 makes it easier:


72/112 = 36/56 = 9/14


Multiplying 9/14 by 100 is no walk in the park either, but it's a little more manageable:

9/14 * 100 =

Rather than multiplying 9 by 100, try to ballpark the reduced value of of 100/14 first. 14 fits into 100 just a bit over 7 times (since 7*14=98), so 100/14 is reduced to slightly over 7.

Multiply by 9: Since 9*7 is 63, the correct answer should be slightly over 63- 64 fits the bill.

[Vish_]

Let the total income be 100,
Then Lee's earnings will be 60 and family earned 40
Now Lee earned 20% more so 60 * 1.20 = 72, but the family's income was the same ie. 40.

So the total family income = 72+40 = 112
Now the % earnings by Lee = 72/112 = 64%