Question

Gaurav has a salary of Rs.21,600 per month. In the first month of the year, he spends 30% of his income on clothing, 20% of the remaining on entertainment and spend some percentage of the remaining on food. He saves 1/3 of what he spends. Find the percentage of spending on food as a % of saving.

Answer 1

21600*30%=6480,15120*20=3024,6480+3024=9504,9504+x/3=

Answer 2

Let x be the amount he spent on food.

21600*30% + 21600*(1-30%)*20% + x + (1/3) * (21600*30% + 21600*(1-30%)*20% + x) = 21600.

Then, you can find x.

Answer 3

Income: 21,600

Spent on Clothes: .30 * (21,600) = 6480

Remaining: 15,120

Spent on Entertainment: .20*6480 = 1,296

Remaining: 13,824

Spent on Food: x% --> (x/100)*13,824 = 138.24*x

Remaining: 13,824 - 138.24*x to be saved
-------------------------

13,824 - 138.24*x (Savings) = 1/3 ( Expenditures)

13,824 - 138.24*x = 1/3( 6480 + 1,296 + 138.24*x )

x = 60.94 or .60% on Food

1/3 or .33% for savings

Find the percentage of spending on food as a % of saving.
------------------------------------------------

Food % / Savings % = .60% / .33% =

@fancy1

Something is not correct with my work.

Answer 4

@Callisto Do you see the first step where my work ran amok? Thanks.

Answer 5

yes.

Answer 6

(A) 19%
(B) 20%
(C) 21%
(D) 30%

Answer 7

Amount spent on entertainment should be .20*(15,120).

Answer 8

x=26784

Answer 9

6480+3024+(6480+3024+x)/3=21600
38010+x=64800
x=26784

Answer 10

24%

Answer 11

right ?

Answer 12

Income: 21,600
Spent on Clothes: .30 * (21,600) = 6480
Remaining: 15,120
Spent on Entertainment: .20*15,120 = 3,024
Remaining: 12,096
Spent on Food: x% --> (x/100)*12,096 = 120.96*x
Remaining: 12,096 - 120.96*x to be saved
-------------
(Savings) = 1/3 ( Expenditures)
12,096 - 120.96*x = 1/3*( 6480 + 3,024 + 120.96*x )
x = 55.36 or .554% for food
Food/Savings = .554/.333 which is incorrect.

Answer 13

@Callisto Do you see my second mistake? And, did you get 24%?

Answer 14

@fancy1

I don't follow this logic:

6480+3024+(6480+3024+x)/3=21600 38010+x=64800

x=26784

Answer 15

I didn't get 24%, but I got 124%...

Answer 16

hey 100-124=24%

Answer 17

24% of saving \(\ne\) 124% of saving

Answer 18

I think 24% is incorrect.

I'm looking at 20% but there is no support that is correct. I don't know what has run amok.

Answer 19

what is this @Callisto i cant understand

Answer 20

Suppose you have $100 as your saving.
24% of your saving is 100* (24/100) = 24
124% of your saving is 100 * (124/100) = 124

Answer 21

Are the options given in the question?

Answer 22

Not by the OP. I found options along with this same question on the Web. One of the options is None of these on one site.

Regardless, there is something I am not seeing in the problem. So, I don't know what to think.

Answer 23

"x = 55.36 or .554% for food"
This part is right.

Food/salary = 0.31
Saving/salary = 0.25
Food/Savings = .31/.25

Answer 24

but ur concept is right?.but it is 24%of 100 in 124 means 24 % extra

Answer 25

got it @Callisto ,@directrix .the percentage of food is 31%

Answer 26

i think the option is none of these

Answer 27

@fancy1 What options were you given with the problem?

Answer 28

u already written

Answer 29

I think something is not right here:

(Savings) = 1/3 ( Expenditures)

--> 12,096 - 120.96*x <--- = 1/3*( 6480 + 3,024 + 120.96*x )

-----------------------------------
12,096 - 120.96*x is the remaining Rs. after expenditures but is not the amount Gaurav

will save.

Answer 30

If he didn't save what he didn't spend after expenditures, then we would have just got an expression in x?!

Answer 31

I agree with that.

Answer 32

\[\frac{12096-120.96x}{\frac{1}{3}(6480+3024+120.96x)}\]

Answer 33

Look at this person's work:

o.0

let monthly income be = x on clothing =.3x on entertainment = .2(.7x) =.14x on food = (.16x)k saving =( .3x .14x .16xk)*1 solving we get k =.31.16 putting the value and we get ...... on the food =.31x ,and saving =.25x % on food / %on saving = .06x/.25x =24% is the correct answer

http://tcyonline.minglebox.com/discuss/ans/5289/gauravs-salary-21600-per-monthfirst-month-year-he-spends-30-his-income-clothing-20-remaining-entertainment-some-perce

Answer 34

.....
0.06 is .31-.25

Answer 35

I know I can get 24% by doing (0.31-0.25)/0.25, but I don't understand why.

Answer 36

I don't follow that, and I have lost faith in my own work. I am going to rest my brain and then start from scratch.

I'm still hung up here in my assumption that the savings is all the money left after expenditutes and is equal to 1/3 the expenditures.

12,096 - 120.96*x = 1/3*( 6480 + 3,024 + 120.96*x )

I suppose there is no reason to assume that he saves all of what he does not spend. lol

Answer 37

I suppose we can make that assumption.

Answer 38

from answer can u get the answer

Answer 39

like x+2=5,ie x=3,means 3+2=5,like that