C.I.	0 - 10	10 - 20	20 - 30
Frequency	15	25	b
Cumulative frequency	15	a	50

Assertion(A): a = 15 + 25 = 40

b = 50 - a

Reason(R): a + 15 = 25

and b = 50 - 10

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.

Cumulative frequency represents the running total of frequencies up to a certain class interval. For instance, the cumulative frequency for the class interval 10–20 includes all frequencies from the previous intervals as well. Therefore, the cumulative frequency for the 10–20 interval is the sum of the frequencies for the 0–10 and 10–20 intervals.

The cumulative frequency for the 10–20 interval is the sum of the frequencies for the 0–10 and 10–20 intervals:

a = 15 + 25 = 40

The cumulative frequency for the 20–30 interval is 50, which includes all previous frequencies. Therefore, the frequency for the 20–30 interval is:

b = 50 - a = 50 - 40 = 10.

∴ A is true, R is false.

Hence, option 1 is the correct option.