a man spent 1/10 of his monthly salary on rent and 5/6 of the remainder on household needs. if $1,800 is left, how much is his monthly salary?

after 1/10, 5/6 of the remainder is 5/6 * 9/10 = 45/60 = 3/4

so, x(1 - 1/10 - 3/4) = 1800
3/20 x = 1800
x = 12000

Solution:

x(1-1/10-5/6)=1800
x-x/10-5x/6=1800
L.c.m=30
30x-3x-25x/30=1800
2x/30=1800
2x=54000
x=27000

1/2

To find out the monthly salary of the man, we can follow these steps:

1. Let's assume the man's monthly salary as "S".

2. According to the given information, he spent 1/10 of his salary on rent, which means he has 9/10 (1 - 1/10) of his salary remaining.

3. After spending on rent, the remaining amount is (9/10)S.

4. Next, he spent 5/6 of the remaining amount on household needs. This means he has 1/6 (1 - 5/6) of the remaining amount left.

5. We are given that $1,800 is left after spending on household needs, which equals 1/6 of the remaining amount ((1/6) * (9/10)S = $1,800).

6. To find the value of S, we need to isolate it in the equation. Multiply both sides of the equation by (10/9) to get:

S = ($1,800 * 6 * 10) / 9

S = $12,000

Therefore, the man's monthly salary is $12,000.