Exercise: 7-E
Assertion- Reason Questions
Q1: Assertion (A): A man bought a new motorcycle for ₹2,50,000. Next year, its price decreased by 10% and further next year, it decreased by 12%. The overall decrease in the price of the motorcycle is 20.8%.
Reason (R): SP = \(\frac{\left(100-loss%\right)}{100}\times\) CP.
Step 1: Use successive loss formula:
Overall % change = \((a + b + \frac{ab}{100})\)%
Where a = −10, b = −12
\[
\text{Net Loss \%} = -10 + (-12) + \frac{(-10)\times(-12)}{100} = -22 + 1.2 = -20.8\%
\]Step 2: Statement (A) is True: Overall decrease is 20.8%.
Step 3: Statement (R) is also True: It’s the correct formula for finding S.P. from C.P. when loss is given.
However, it does not explain the successive loss calculation.
Answer: b. Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
Q2: Assertion (A): Selling price of 9 articles is equal to the cost price of 15 articles. In this transaction, there is a profit of \(66\frac{2}{3}\)%.
Reason (R): Gain% = \(\frac{Actual\ gain}{100}\times\ C.P.\)
Step 1:
Let the cost price (C.P.) of 1 article = ₹1
⇒ Cost price of 15 articles = ₹15
Given: Selling price (S.P.) of 9 articles = ₹15
⇒ Selling price of 1 article = ₹15 ÷ 9 = ₹1.666…
Step 2:
C.P. of 1 article = ₹1
S.P. of 1 article = ₹1.666…
Profit = S.P. – C.P. = ₹1.666… – ₹1 = ₹0.666…
Step 3:
Gain% = \(\frac{\text{Profit}}{\text{C.P.}} \times 100\)
= \(\frac{0.666…}{1} \times 100 = 66.66…\)%
= \(66\frac{2}{3}\)% ✅
Step 4:
Check the Reason (R):
Reason given: Gain% = \(\frac{\text{Actual gain}}{100} \times \text{C.P.}\)
This is an incorrect formula.
✅ The correct formula is:
Gain% = \(\frac{\text{Actual gain}}{\text{C.P.}} \times 100\)
Conclusion:
Assertion (A) is ✅ True
Reason (R) is ❌ False
Answer: c. Assertion (A) is true but Reason (R) is false.
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