After taxes, Sally takes home a salary of J = $5000 every month.

Question

After taxes, Sally takes home a salary of J = $5000 every month. She pays P percent of this to her rent and all her fixed bills each month, leaving her with K left. She spends half of K on groceries, leaving her with L left. If she spends $\frac{1}{3}$ of L on gifts and puts $\frac{2}{5}$
of L into her savings account, this would leave her with $200 for miscellaneous expenses. What is the value of P?

A. 30
B. 40
C. 50
D. 60
E. 70

A. 30
B. 40
C. 50
D. 60
E. 70

Kurtosis · Accepted Answer

L - (1/3 + 2/5)L = 200 --> L = 750

L = K/2 --> K = 1500

P = ((5000 - 1500)/5000)*100 = 70

Answer: E

pushpitkc · Answer

If we translate the question into equations, we will the following 3 equations
 5000 - \frac{P}{100}*5000 = K  ->  5000 - 50P = K  ->(1)
 \frac{K}{2} = L  -> (2)
 \frac{L}{3} + \frac{2L}{5} + 200 = L  -> (3)

Solving the third equation, we get 
 \frac{L}{3} + \frac{2L}{5} + 200 = L  ->  L - \frac{L}{3} - \frac{2L}{5} = 200  ->  \frac{15L - 5L - 6L}{15} = 200  ->  \frac{4L}{15} = 200

Substituting  L = \frac{K}{2} , we will get  \frac{2K}{15} = 200  ->  K = 1500

Substituting this value of K in the first equation, we get 
 5000 - 50P = 1500  ->  50P = 3500  ->  P = \frac{3500}{50} = 70

Therefore, the value of P is  70(Option E)

akadiyan · Answer

We can solve this by backtracking starting from the known numbers.

Step 1: Calculate L
33.33% of L Spent on Gifts , 40% of L spent on savings , balance = 26.67% 
We know that 26.67% is 200$, So 100% of L is 750$

Step 2: Calculate K
K is twice the amount of L. 
L=750 , so K = 1500.

Step 3: Calculate P
P % is the amount paid for Rent and Bills = 5000$-1500$ = 3500$ 
3500$ is 70% of 5000.

Ans:   E

ScottTargetTestPrep · Answer

Instead of solving the problem algebraically, let’s make an educated guess for the value of P. Let’s guess P = 40 and check whether it satisfies all the criteria of the problem.

If P = 40, Sally pays 0.4 x 5000 = $2000 for rent and all her fixed bills, leaving her with 5000 - 2000 = $3000 (i.e., K = 3000). She then spends ½ x 3000 = 1500 on groceries, leaving her with 3000 - 1500 = $1500 (i.e., L = 1500). She then spends ⅓ x 1500 = $500 on gifts and puts ⅖ x 1500 = $600 into her savings account. This would leave her with 1500 - 500 - 600 = $400 for miscellaneous expenses. However, since we are given that she is left with only $200, we see that 40 is not the correct answer.

Let’s try P = 70.

If P = 70, Sally pays 0.7 x 5000 = $3500 for rent and all her fixed bills, leaving her with 5000 - 3500 = $1500 (i.e., K = 1500). She then spends ½ x 1500 = 750 on groceries, leaving her with 1500 - 750 = $750 (i.e., L = 750). She then spends ⅓ x 750 = $250 on gifts and puts ⅖ x 750 = $300 into her savings account. This would leave her with 750 - 250 - 300 = $200 for miscellaneous expenses. Since this matches the dollar amount of her miscellaneous expenses, we see that P = 70.

(Note: The reason we try 40 and 70 first is because of the dollar amount for K. Notice that K would be 3000 and 1500, respectively, which are numbers for which we can easily take ½, ⅓ and ⅖ of. Had we used P = 50, we see that K would have been 2500, which is not easily divided by 3.)

Answer: E

WizakoMani · Answer

This question is conceptually simple. However it does take some additional time than an average question of this difficulty.

Interpret the given question as equations.

Statement 1: She pays P percent of this to her rent and all her fixed bills each month, leaving her with K left.
 5000 - \frac{P}{100}5000 = K

Statement 2: She spends half of K on groceries, leaving her with L left.
She spends half of K and the remaining half is equal to L
 \frac{K}{2} = L

Statement 3: If she spends  \frac{1}{3}  of L on gifts and puts  \frac{2}{5} ​​ of L into her savings account, this would leave her with $200 for miscellaneous expenses.

L - \frac{1}{3}L - \frac{2}{5}L = 200$

Taking LCM, we get  \frac{4L}{15} = 200 
 L = 750

L = \frac{K}{2} --> K = 1500

5000 - \frac{P}{100}5000 = K 
 5000 - \frac{P}{100}5000 = 1500 
 5000 - 1500 = \frac{P}{100}5000 
 3500 = \frac{P}{100}5000 
 \frac{350000}{5000} = P

P = 70

Option(E) is the correct answer

Kinshook · Answer

Given: After taxes, Sally takes home a salary of J = $5000 every month. She pays P percent of this to her rent and all her fixed bills each month, leaving her with K left. She spends half of K on groceries, leaving her with L left. If she spends  \frac{1}{3}  of L on gifts and puts  \frac{2}{5} ​​ of L into her savings account, this would leave her with $200 for miscellaneous expenses.

Asked:What is the value of P?

Salary J = $5000
Rent = P%*J = 50P
K = 5000 - 50P = 50 (100-P)
Groceries = 50/2 (100-P) = 25(100-P)
L = 25(100-P)

Spend on gifts = L/3
Savings =2L/5

Miscellaneous expenses = L - L/3 - 2L/5 = (15-5-6)L/15 = 4L/15 = 4*25(100-P)/15 = $200 
100 - P = 30
P = 70

IMO E

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After taxes, Sally takes home a salary of J = $5000 every month.

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After taxes, Sally takes home a salary of J = $5000 every month.

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