Discussion
Three brands of pens A, B and C are available in packets of 10, 12 and 24 respectively. If a shopkeeper wants to buy equal number of pens of each brand, what is the minimum number of packets of each brand, he should buy ?
Answer: D
He should buy A = 12, B = 10, C = 5 packets.
The smallest equal number of pens is the LCM of the packet sizes:
\[ \begin{aligned} 10 &= 2 \times 5,\quad 12 = 2^{2} \times 3,\quad 24 = 2^{3} \times 3 \\ \text{LCM} &= 2^{3} \times 3 \times 5 = 120 \end{aligned} \]
So he needs 120 pens of each brand: 120/10 = 12 packets of A, 120/12 = 10 of B and 120/24 = 5 of C. The other options swap the packet counts between brands; for example A = 10 would give only 100 pens of brand A.
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