Framing Algebraic Expressions — Assertion-Reason Type Questions

Assertion (A): The sum of two consecutive multiples of 4 is 100. The smaller number is 48.

Reason (R): If the smaller number is $x$, then $(x) + (x + 4) = 100$.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

Two consecutive multiples of 4 differ by 4. Taking the smaller multiple as $x$, the next is $x + 4$.

$\Rightarrow x + (x + 4) = 100 \\[1em] \Rightarrow 2x + 4 = 100 \\[1em] \Rightarrow 2x = 96 \\[1em] \Rightarrow x = 48.$

So the smaller number is 48, which means Assertion (A) is true.

The equation used, $(x) + (x + 4) = 100$, is exactly the correct setup that leads to the answer, so Reason (R) is true.

Hence, option 3 is the correct option.

Assertion (A): $x = 2$ is the solution of the linear equation : $5 - x = \dfrac{x}{2} + 2$

Reason (R): On substituting $x = 2$ if the values of L.H.S. and R.H.S. come equal, $x = 2$ is solution of the given equation.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

Substituting $x$ = 2 in the given equation 5 − $x = \dfrac{x}{2}$ + 2 :

L.H.S. = 5 − 2 = 3

R.H.S. = $\dfrac{2}{2}$ + 2 = 1 + 2 = 3

Since L.H.S. = R.H.S., $x$ = 2 is a solution. So, Assertion (A) is true.

Reason (R) correctly states the method of checking a solution by substitution. So, Reason (R) is true.

Hence, option 3 is the correct option.