Linear Equations and Inequalities in One Variable — Statement I-II Type Questions

Statement I: If $4y - 3 = 7y + 2$, then $y = -1$

Statement II: We can add or subtract the same expression to both sides of a linear equation.

1. Statement I is true but Statement II is false.

2. Statement I is false but Statement II is true.

3. Both Statement I and Statement II are true.

4. Both Statement I and Statement II are false.

Answer

Solving,

$\Rightarrow 4y - 3 = 7y + 2 \\[1em] \Rightarrow - 3 - 2 = 7y - 4y \\[1em] \Rightarrow 3y = - 5 \\[1em] \Rightarrow y = - \dfrac{5}{3}$

As $y = -\dfrac{5}{3}$ and not -1, Statement I is false.

We can add or subtract the same expression to both sides of a linear equation, so Statement II is true.

Hence, option 2 is the correct option.

Statement I: If $2(x - 3) = 10$, then $x = 8$

Statement II: We can multiply or divide both sides of a linear equation by any non-zero expression.

1. Statement I is true but Statement II is false.

2. Statement I is false but Statement II is true.

3. Both Statement I and Statement II are true.

4. Both Statement I and Statement II are false.

Answer

Solving,

$\Rightarrow 2(x - 3) = 10 \\[1em] \Rightarrow 2x - 6 = 10 \\[1em] \Rightarrow 2x = 10 + 6 \\[1em] \Rightarrow 2x = 16 \\[1em] \Rightarrow x = \dfrac{16}{2} \\[1em] \Rightarrow x = 8$

As $x = 8$, Statement I is true.

We can multiply or divide both sides of a linear equation by any non-zero expression, so Statement II is true.

Hence, option 3 is the correct option.

Statement I: If a shopkeeper purchases a table for ₹1,000 and he wants to make a profit of atleast 20% on it, he must sell it for greater than ₹1,100.

Statement II: Profit % is calculated on the cost price.

1. Statement I is true but Statement II is false.

2. Statement I is false but Statement II is true.

3. Both Statement I and Statement II are true.

4. Both Statement I and Statement II are false.

Answer

Given, cost price of the table = ₹ 1,000

Profit required = atleast 20% of the cost price

⇒ Profit = $\dfrac{20}{100} \times 1,000$ = ₹ 200

So, selling price = 1,000 + 200 = ₹ 1,200

As the shopkeeper must sell the table for atleast ₹ 1,200 and not for greater than ₹ 1,100, Statement I is false.

Profit % is always calculated on the cost price, so Statement II is true.

Hence, option 2 is the correct option.