Unitary Method — Assertion-Reason Questions

Assertion (A): If the cost of 15 pens is ₹180, then the cost of 7 pens is ₹84.

Reason (R): For finding the values of a given number of units, we first find the value of 1 unit.

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

3. Assertion (A) is true but Reason (R) is false.

4. Assertion (A) is false but Reason (R) is true.

Answer

Cost of 15 pens = ₹ 180

Cost of 1 pen = ₹ $\Big(\dfrac{180}{15}\Big)$ = ₹ 12 [Less pens, Less cost]

Cost of 7 pens = ₹ (12 x 7) = ₹ 84 [More pens, More cost]

So, Assertion (A) is true.

For finding the values of a given number of units, we first find the value of 1 unit.

So, Reason (R) is true and is the correct explanation of Assertion (A), since the cost of 7 pens is found by first finding the cost of 1 pen.

Hence, option 1 is the correct option.

Assertion (A): If a car travels 252 km in 6 hours, then it will travel 200 km in 5 hours.

Reason (R): Distance travelled by a car is directly proportional to the time it runs.

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

3. Assertion (A) is true but Reason (R) is false.

4. Assertion (A) is false but Reason (R) is true.

Answer

In 6 hours, the car travels = 252 km

In 1 hour, the car travels = $\Big(\dfrac{252}{6}\Big)$ km = 42 km [Less time, Less distance]

In 5 hours, the car travels = (42 x 5) km = 210 km [More time, More distance]

Since 210 km ≠ 200 km, Assertion (A) is false.

Reason (R) is true, as distance travelled by a car is directly proportional to the time it runs.

Hence, option 4 is the correct option.