Let the food in the boy's home be : F
Given : This food is sufficient for 50 children for 12 days
[tex]\implies \sf{\textsf{The food consumed by 50 children in one day} : \dfrac{F}{12}}[/tex]
[tex]\implies \sf{\textsf{The food consumed by 1 child in one day} : \dfrac{F}{12 \times 50}}[/tex]
Given : There is an increase of 10 more children
It means : Total children = 60
[tex]\implies \sf{\textsf{The food consumed by 60 children in one day} : \dfrac{F \times 60}{12 \times 50}}[/tex]
[tex]\implies \sf{\textsf{The food consumed by 60 children in one day} : \dfrac{F}{10}}[/tex]
[tex]\implies \sf{\textsf{The food consumed by 60 children in 10 days} : \dfrac{F\times 10}{10}}[/tex]
[tex]\implies \sf{\textsf{The food consumed by 60 children in 10 days} : F}[/tex]
Answer: The food is sufficient for 10 days
