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 ?

The correct option is A = 12, B = 10, C = 5.

Step 1: Understand the given information
Brand A pens come in packets of 10.
Brand B pens come in packets of 12.
Brand C pens come in packets of 24.
The shopkeeper wants to buy an equal total number of pens for each of the three brands using the minimum number of packets.

Step 2: Find the total number of pens required for each brand
To buy an equal number of pens of each brand, the total number of pens of each brand must be a common multiple of 10, 12, and 24. To minimize the number of packets, we find the Least Common Multiple (LCM) of 10, 12, and 24.

Let's write down the prime factorization of each number:

$10=2\times 5$

$12=2^2\times 3$

$24=2^3\times 3$

Taking the highest power of each prime factor involved (2³, 3¹, and 5¹):

$\text{LCM}(10,12,24)=2^3\times 3\times 5=8\times 3\times 5=120$

So, the shopkeeper must buy 120 pens of each brand.

Step 3: Calculate the minimum number of packets for each brand

For Brand A:
Number of packets = $\frac{120}{10}=12$

For Brand B:
Number of packets = $\frac{120}{12}=10$

For Brand C:
Number of packets = $\frac{120}{24}=5$

Thus, the minimum number of packets to buy for each brand is A = 12, B = 10, C = 5.