Questions & Answers

Question

Answers

A. \[Rs.\,{\rm{ 6}}\]

B. \[Rs.{\rm{ 5}}{\rm{.50}}\]

C. \[Rs.{\rm{ 5}}\]

D. \[Rs.{\rm{ 6}}{\rm{.50}}\]

Answer
Verified

Here, it is given that the total cost of 10 erasers and 5 sharpeners is at least\[Rs.{\rm{ }}65\]. And. the cost of each eraser cannot exceed \[Rs.{\rm{ }}4\].

We have to find the minimum possible cost of sharpener.

Let us cost one eraser to be \[e\] and the cost of one sharpener to be \[s\] respectively.

According to question,

We can write and mark it by equation (1)

\[65\; < {\rm{ }}10e{\rm{ }} + {\rm{ }}5s\]………….. (1)

Again, cost of eraser cannot exceed

\[e\; \le {\rm{ }}4{\rm{ }}\]……………………… (2)

Multiply both side by 10 in equation (2)

\[10e{\rm{ }}\; \le {\rm{ }}40\;\]…………………… (3)

Now let us add \[5s\] on both sides of the inequality (3) we get

\[10e + 5s{\rm{ }}\; \le {\rm{ }}40\; + 5s\]…………. (4)

By comparing (1) and (4) we get,

\[65{\rm{ < }}10e + 5s \le {\rm{ }}40 + {\rm{ }}5s\]

From the above equation we get,

\[65{\rm{ < }}40 + {\rm{ }}5s\]

By solving the above equation we get,

\[65 - 40{\rm{ < }}5s\]

On subtracting the left hand side of the above equation we get,

\[25{\rm{ < }}\;\;5s\]

Let us divide the above inequality by 25 both sides we get,

\[s{\rm{ > }}\dfrac{{25}}{5}\]

That is \[s{\rm{ > }}5\]

Therefore, the minimum price of a sharpener is \[Rs.{\rm{ }}5\]