Spending Monthly Salary

Rajesh"s salary =x spent on clothes = x/3 remaining =2x/3 spent on treat=1/5 of 2 x/3 remaining =4/5 of 2 x/3 spent on trip =1/4 of 4/5 of 2 x/3 remaining =3/4 of 4/5 of 2 x/3 =2 x/5 =100 x =500/2 =250

Let x be the total salary, so

Spent on clothing = 1/3 x, and 2/3 x is left

Spent on treat = 1/5 of 2/3 x, or 2/15 and 8/15 x is left

Spent on trip= 1/4 of 8/15x

So

x - 1/3 x - 2/15 x - 2/15 x = 100,

(15-5-4)x= 1500, or , x=250

Assume his salary is " x " when he spent 1/3 from it's salary so the remaining money is x- 1/3 x = 2/3 x then he spent 1/5 from the remaining money so we should know 1/5 from 2/3 x .. and it will be (1/5 ) ( 2/3 x) = 2/15 x so (2/3 x ) - (2/15 x) =(8/15 x) which is the remaining money .. then he spent 1/4 from the remaining money with the same way >> (1/4) (8/15 x) =(2/15 x) so (8/15 x) - (2/15 x) = (2/5 x) which is the remaining money .. as he told us that the remaining money = 100 so 2/5 x = 100 >>> so " x " = 250 which is the money he had in the beginning .

let us consider total amount be x then the amount he spend on clothes will be x/3 remaining amount x-x/3=2x/3 of which he spent 1/5th for meal =2x/15 remaining amount=2x/3-2x/15=8x/15 of which he spent 1/4th on trip=2x/15 amount left=6x/15=2x/5=100(since given) there fore x=250

At first he spend 1/3 of his money meaning he has 2/3 of his money left. 2/3 will then be multiplied to 4/5 because it will represent his money left after spending 1/5 treating his friends to a meal, so now he will only have 8/15 of his money left. 8/15 will then be multiplied to 3/4 representing his money left after spending 1/4 on a trip nearby island, therefore he will now have 2/5 of his money left which is equivalent to Rs 100; and so to find the money with him at the beginning we will just divide 100 by 2 and multiply it by 5 and now we have Rs 250. :)

Let total money=x therefore money expended on clothes=x/3 money remaining=2x/3 money expended on treat=(2x/3) 1/5=2x/15 money remaining=(2x/3)-(2x/15)=8x/15 money expended on trip=(8x/15) 1/4=8x/60 money remaining=(8x/15)-(8x/60)=100=24x/60 solve for x

Let salary = x, Clothes = x/3; Remaining = x-x/3 = 2x/3 Treat = (1/5) (2x/3) = 2x/15; Remaining = 2x/3 - 2x/15 = 8x/15 Trip = (1/4) (8x/15) = 2x/15; Remaining = 8x/15 - 2x/15 = 6x/15 = 2x/5 = 100 Implies x = 250

Let initially he has Rs. x

Now he spent 1/3 of the total on clothes. Therefore he left with Rs. (X-X/3) i.e. Rs. 2x/3.

Now he spent 1/5 of the remaining on meal i.e. Rs. 2x/15. Therefore he left with Rs. (2x/3 - 2x/15) i.e. Rs. 8x/15.

Now he sent 1/4 of remaining on trip i.e. Rs. 2x/15.

Now he left with Rs. 100

Therefore, an equation can be formed as :

x - ( x/3 + 2x/15 + 2x/15 ) = 100

x - ( 9x/15 ) = 100

6x = 1500

x = 250

Therefore, he have Rs . 250 in the begining.

LET TOTAL SALARY BE Rs. ''X''. HE SPENT 1/3 ON CLOTHES. NOW HE HAVE Rs. ''2X/3''. NOW HE SPENT 1/5 OF REMAINING TO TREAT HIS FRIEND THAT IS Rs. ''2X/15''. NOW HE HAVE Rs. ''8X/15''. NOW HE SPENT 1/4 OF IT ON A TRIP, WHICH IS Rs. ''2X/15''. AT LAST HE SAVED Rs. ''6X/15'' WHICH IS EQUAL TO 100.

                     6X/15 = 100

                     6X =  100 * 15

                      6X = 1500

                       X = 1500/6  = 250

1/3. 1/5. 1/4.x = 100 x =250 Hence, the answer.

let us initial value x.---2x/3 4/5(remaining of 1/5) 3/4(remaining of 1/4)=100 so x=250

100.4/3.5/4.3/2 = 250

Imagine the total salary as 100%:

-After Rajesh has spent 1/3, 2/3 rested (1 - 1/3), he has about 66,66% yet; -With the meal he still had about (2/3 (1-1/5))=2/3 4/5 = 8/15 ; -The trip cost 1/4 of the left, 8/15 (1-1/4)=8/15 3/4=24/60;

If 100 is 24/60 of the salary, 60/60 is:

100% salary = 100/(24/60) = R$ 250

After spending 1/3 rd on clothes, 2/3 rd remain. Of 2/3 rd, 1/5 is spent on treat. So, 4/5th of 2/3rd or 8/15th remain. Again, 1/4th of 8/15 is spent on trip, so, 3/4th of 8/15 or 2/5th remains. This 2/5th is equal to Rs.100. So, the starting amount was 5/2 * 100 = Rs.250

Step 1: Consider 'x' to be the total income

Step 2: Calculate the total expenses :- (1/3)x + {(2/3)x (1/5)} + {(4/5) (2/3)x*(1/4)}

Calculation: x - [(1/3)x + {(2/3)x (1/5)} + {(4/5) (2/3)x*(1/4)}] = 100 (x-total expenses = 100)

Therefore, x = 250 /- (ANS)

LEt man^' s salary=s clothing=(1 s)/3
left after=s-(1
s)/3 =(2 s)/3
1/5 times of left over spent on Meal=(2
s)/15
then remains=(8 s)/15
1/4 times of remains ontrip=(2
s)/15 lastly remaining=(6 s)/15 that is=100 thus (6 s)/15=100≫ s=250

250

The answer is 250. It is arrived at by simple exclusions. No complex method needed.

let x = original price x - 1/3 (x) - 2/3(1/5)(x) - 2/3(4/5)(1/4) x = 100 (15x - 5x -2x -2x)/15 = 100 6x/15 = 100 6x = 1500 x=250

(1-1/3 1-1/5 1-1/4)*X=100, then X=250 Left terms always be subtracted from total (assuming)

X . (2/3) . (4/5) . (3/4)=100 The Dot represent multiplication.

Let S$ be the salary,first he spends (1/3)S on cloths,he left with (2/3)S, next he spends 1/5 of remaining salary on meals i e (1/5)(2/3)S on meals,he left with (2/3)(1-1/5)S=(8/15)S. lastly he spends 1/4th of remaining amount on travel i e (1/4)(8/15)S,finally he left with (8/15)(1-1/4)S=(2/5)S=100. S=500/2=250$.

"a" is the all of Rajesh monthly salary, "b" is the second after the wardrobes improvement, "c" the money after the treat, and "d" after the trip to the island.

a = all the Monthly salary

b = a - 1/3a

c = b - 1/5b

d = c - 1/4c = 100

So, we do it from the last money

• 100 = c - 1/4c

  100 = 4c - c x 1/4

  100 = 3/4c

  c = 400/3

• 400/3 = b - 1/5b

  400/3 = 5b - b x 1/5

  4b = 2000/3

  b = 500/3

• 500/3 = a - 1/3a

  3a - a = 500/3 x 3

  2a = 500

  a = 500/2 = 250

• a = all the monthly salary = 250

250

let x be the monthly salary of Rajesh. amount spent on clothes = x/3. Remaining amount after spending on clothes = 2x/3. amount spent on treating friends = 1/5 of (2x/3) = 2x/15. amount left after treating friends = 2x/3 - 2x/15 = 8x/15. amount spent on trip = 1/4 of (8x/15) = 8x/60. total amount spent = x/3 + 2x/15 + 8x/60 = 36x/60. amount remaining = 24x/60. 24x/60 = 100, which implies x = 250

250/3=83 so balance is 167

167/5=33 so balance is 134

134/4=34 so balance is 100

x/3+2x/15+8x/60+100=x on solving this we get 250

x = what he had at the beginning.

• He spent $\frac{1}{3}$ of it on clothes to improve his wardrobe => x - $\frac{1}{3}$ x = a.
• He spent $\frac{1}{5}$ of the remaining to treat his friends to a meal => a - $\frac{1}{5}$ a = b.
• Of what's left, he spent $\frac{1}{4}$ of it on a trip to a nearby island => b - $\frac{1}{4}$ b = c.
• He was left with Rs. 100 => from above we can conclude that c=100.

so $\frac{3}{4}$ b = 100 therefore b= $\frac{400}{3}$

then $\frac{4}{5}$ a = $\frac{400}{3}$ therefore a= $\frac{500}{3}$

last $\frac{2}{3}$ x = $\frac{500}{3}$ therefore x = 250

so he had Rs. 250 in the beginning...

hope this is easy to understand.. :)

assume the salary is 100 divide in to three part as one third was spent on cloths that is 33.33 balance remaining 100-33.33= 66.66 divide the balance in to fifth parts used for treat which is 13.33 balance remaining 53.33 of which he spent fourth part on trip that is 13.33 balance remains 40% of his salary which is Rs.100

therefor X=100*100/40=250

I went backwards. So he had one hundred dollars, which was 3/4 of what he had when decided to visit the island: (3/4)z=100 z=(400/3) That gets us to the meal. Again, same process, he spend 1/5, so 4/5 was left to him giving us: (4/5)y=(400/3) y=(5 400)/(4 3) simplifies too... y=(5 100)/3 Now we're at the clothes. He spent 1/3, so 2/3 remained, meaning that: (2/3)x=(5 100)/3 x=(3 5 100)/(3 2) simplifies to... x=5 50=250 So he started out with $250, and we're done! :)