The product of two 2-digit numbers is 1938 . If the product of their unit’s digits is 28 and that of ten’s digits is 15 , find the larger number. (a) 34 (b) 57 (c) 43 (d) 75

Correct Answer

Given the product of the unit’s digits is 28 and the product of the ten’s digits is 15, we determined:

• The unit’s digits can only be 4 and 7 since \(4 \times 7 = 28\).
• The ten’s digits can only be 3 and 5 since \(3 \times 5 = 15\).

This analysis provides us with two potential pairs of numbers based on the combinations of the ten’s and unit’s digits:

• 34 and 57
• 37 and 54

After calculating the products:

• \(34 \times 57 = 1938\)
• \(37 \times 54 = 1998\), which does not match the given product.

The calculations confirm that \(34 \times 57 = 1938\), aligning perfectly with the given conditions.

Therefore, the larger number among the two is 57.

The correct answer is (b) 57.