Let's denote Anil's monthly income as "I".
According to the information given:
- He spent 1/4 of his income on food, which is (1/4) * I.
- He spent 2/5 of his income on other expenses, which is (2/5) * I.
- He donated 1/6 of his income for the education of orphan children, which is (1/6) * I.
The total amount he spent on these expenses and donations is:
(1/4) * I + (2/5) * I + (1/6) * I
To find the amount he was left with, we need to subtract this total from his total income:
I - [(1/4) * I + (2/5) * I + (1/6) * I]
Given that he was left with Rs. 10,000, we can set up the equation:
I - [(1/4) * I + (2/5) * I + (1/6) * I] = 10,000
Let's solve for I:
I - [(15/60) * I + (24/60) * I + (10/60) * I] = 10,000
I - [(49/60) * I] = 10,000
(11/60) * I = 10,000
Now, solve for I:
I = (10,000 * 60) / 11
I = 54,545.45
Anil's monthly income is approximately Rs. 54,545.45.