The simple interest earned on ₹2,800 at a rate of 10\% per annum for 3 years is ₹x and ₹1,736 is the simple interest earned on ₹6,200 at a rate of 14\% for y years, then the value of $\frac{x}{y}$ is:

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**Solution:**

1. Calculate simple interest for the first condition:
   - Principal, $P_1 = 2800$
   - Rate, $r_1 = 10\%$
   - Time, $t_1 = 3$ years

Using the formula:
   $$	ext{Simple Interest} = \frac{P 	imes r 	imes t}{100}$$

$$x = \frac{2800 	imes 10 	imes 3}{100} = 840$$

2. Calculate time $y$ for the second condition:
   - Principal, $P_2 = 6200$
   - Rate, $r_2 = 14\%$
   - Simple Interest, $S.I. = 1736$

Using the formula:
   $$1736 = \frac{6200 	imes 14 	imes y}{100}$$

Solve for $y$:
   $$y = \frac{1736 	imes 100}{6200 	imes 14} = 2 	ext{ years}$$

3. Calculate the required ratio:
   $$\frac{x}{y} = \frac{840}{2} = 420$$

**Answer:** $420$

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