M and N start a business. M invests ₹79,000 more than N for 7 months and N invests for 6 months. M’s share is ₹745 more than that of N, out of a total profit of ₹6,705. Find the capital contributed by M.

Let N’s capital be ₹$x$.
Then M’s capital = ₹$(x + 79{,}000)$

Time periods:
M → 7 months, N → 6 months

Profit ratio:
$(x + 79{,}000)\times 7 : x \times 6$

Given total profit = ₹6705 and M gets ₹745 more than N.

Let N’s share = ₹$y$, then M’s share = ₹$(y + 745)$

$y + (y + 745) = 6705$
$2y + 745 = 6705$
$2y = 5960 \Rightarrow y = 2980$

So,
N’s share = ₹2980
M’s share = ₹3725

Thus ratio:
$3725 : 2980 = 5 : 4$

Now,
$\frac{(x + 79{,}000)\times 7}{x \times 6} = \frac{5}{4}$

$\frac{7(x + 79{,}000)}{6x} = \frac{5}{4}$

Cross multiply:
$28(x + 79{,}000) = 30x$

$28x + 22{,}12{,}000 = 30x$

$22{,}12{,}000 = 2x \Rightarrow x = 11{,}06{,}000$

So, M’s capital:
$x + 79{,}000 = 11{,}85{,}000$

Final Answer: ₹11,85,000