Assertion-Reason Questions
Q1: Assertion (A): If \(\frac{m}{3}+1=\frac{7}{15}\), then \(\frac{m}{3}=\frac{7}{15}-1\).
Reason (R): Transposition is the process in which any term Of an equation may taken to the other side with sign changed.
Step 1:Check the Assertion:
\(\frac{m}{3}+1 = \frac{7}{15}\)
Subtract 1 from both sides (transposition):
\[
\frac{m}{3} = \frac{7}{15} – 1
\]
✅ Assertion is **true**.
Step 2:Check the Reason:
Transposition is exactly the method used here to move +1 to the other side as -1.
✅ Reason is **true**.
Step 3:Does Reason explain Assertion?
Yes, the step in Assertion uses transposition. Therefore, Reason **correctly explains** Assertion.
Answer: a. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
Q2: Assertion (A): Two numbers differ by 40. When each number is increased by 8, the bigger number becomes thrice the smaller number. If one number is x, then the other number is \(\left(40-x\right)\).
Reason (R): Solving an equation means finding all its solutions (roots).
Step 1:Let the numbers be \(x\) and \(y\), where \(y\) is bigger.
Difference: \(y – x = 40 \\
y = x + 40\)
Step 2:According to the problem, when 8 is added to each:
\[
y + 8 = 3(x + 8)
\]
Substitute \(y = x + 40\):
\[
x + 40 + 8 = 3(x + 8) \\
x + 48 = 3x + 24 \\
48 – 24 = 3x – x \\
24 = 2x \\
x = 12
\]Step 3:Then the other number \(y = x + 40 = 12 + 40 = 52\)
❌ The Assertion says the other number is \(40 – x = 28\), which is **incorrect**.
Hence, Assertion is **false**.
Step 4:Reason is a correct general statement about solving equations, so Reason is **true**.
Answer: d. Assertion (A) is false but Reason (R) is true
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