Question

Lilly is preparing dinner plates. She has 12 samosas and 16 rolls. If she wants to make all the plates identical without any food left over, what is the greatest number of plates Lilly can prepare ?

• A. 4
• B. 5
• C. 7
• D. 3

Answer 1

The correct option is A 4

To make all the plates identical and find the greatest number of plates, we have to find the greatest number which can divide 12 and 16 exactly.

That is nothing but H.C.F of 12 and 16.

12 = $2\times 2\times 3$
16 = $2\times 2\times 2\times 2$

Greatest factor is $2\times 2=4$

H.C.F of 12, 16 = 4

$\therefore$ 12 samosas would be served in 4 plates at the rate of 3 pieces per plate.

And 16 rolls would be served in 4 plates at the rate of 4 rolls per plate.

In this way, each of the 4 plates would have 3 samosas and 4 rolls. And all the 4 plates would be identical.

$\therefore$ greatest number of plates Lilly can prepare is 4