A and B invested ₹1,20,000  and ₹1,60,000 respectively.

Explanation

Profit is divided in the ratio of Investment × Time.

A's investment-time:
$1,20,000 \times 10 = 12,00,000$
B's investment-time:
$1,60,000 \times 7 = 11,20,000$
Therefore, the profit-sharing ratio is:
$12,00,000 : 11,20,000 = 15 : 14$
So, B's share is 14 parts = ₹16,800.
Therefore, 1 part:
$\frac{16800}{14} = ₹1200$
Total profit corresponds to 15 + 14 = 29 parts.
Total profit:
$29 \times 1200 = ₹34,800$
Answer: ₹34,800