Question

There were 35 studentsina hostel.Ifthenumber of studentsbe increased by 7, the expenditure on food increases by Rs 42 per day while the average expenditure of studentsis reduced by Rs 1. What was the initial expenditure on food per day?

A) Rs 432 B) Rs 442 C) Rs 420 D) Rs 400

Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

Let us assume That, original average expenidture was Rs.x .

Than,

→ Average Expenditure = Rs.x

→ Total students = 35

→ Total Expenditure = 35 * x = 35x

Now,

→ Average Expenditure = (x - 1)

→ Total students = 35 + 7 = 42

→ Total Expenditure = 42(x - 1)

Therefore,

→ 35x + 42 = 42(x - 1)

→ 35x + 42 = 42x - 42

→ 42x - 35x = 42 + 42

→ 7x = 84

→ x = Rs.12

So,

→ Initial expenditure = 12 * 35 = Rs.420 (C) (Ans.)

Hence, The Initial expenditure on Food per day was Rs.420.

Answer 2

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

• There were 35 students in hostel.
• If the number of students be increased by 7.
• then the expenditure on food increases by Rs 42 per day.
• While. the average expenditure of students is reduced by Rs1.

${\bf{\blue{\underline{To\:Find:}}}}$

• Intial expenditure on food per day.

${\bf{\blue{\underline{Now:}}}}$

• Let the original average expenditure was = n
• and the total expenditure = 35n

$\dagger \: \: \underline{ \underline{\frak{ according \: to \: the \: question : }}}$

$: \implies{\sf{ 35n + 42 = (n - 1) \times 42}}$

$: \implies{\sf{ 35n + 42 = 42n - 42}}$

$: \implies{\sf{ 35n -42 n= -42 - 42}}$

$: \implies{\sf{ -7n= -84}}$

$: \implies{\sf{ n= \frac{ - 84}{ - 7} }}$

$: \implies{\sf{ n= \frac{ \cancel{84} }{ \cancel 7} }}$

$: \implies{\sf{ n= 12}}$

$\dagger \: \underline{\boxed {\sf{Hence, \: the \: intial \: expenditure = 35 \times 12 = 420}}}$

$\bigstar \: \underline{ \underline {\frak{Option \: (c) \: is \: correct.}}}$