Percentage and its Applications — Statement I-II Type Questions

Statement I: Profit % or loss % is always calculated on CP.

Statement II: When the selling price is greater than the cost price, the seller incurs a loss.

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

Profit percentage = $\dfrac{\text{Profit}}{\text{C.P.}} \times 100$% and loss percentage = $\dfrac{\text{Loss}}{\text{C.P.}} \times 100$%

In both the formulae, the cost price is taken as the base.

So, Statement I is true.

When the selling price is greater than the cost price, the seller makes a profit and not a loss.

So, Statement II is false.

Hence, option 1 is the correct option.

Statement I: If the SP of an item is doubled, then the profit % also doubles.

Statement II: If the CP of an item is halved, then the profit % doubles.

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

Let the C.P. of an item be ₹100 and its S.P. be ₹150.

Profit = ₹150 - ₹100 = ₹50

Profit percentage = $\dfrac{50}{100} \times 100$% = 50%

On doubling the S.P., new S.P. = 2 x ₹150 = ₹300

New profit = ₹300 - ₹100 = ₹200

New profit percentage = $\dfrac{200}{100} \times 100$% = 200%

As 200% ≠ 2 x 50%, the profit percentage does not double.

So, Statement I is false.

On halving the C.P., new C.P. = $\dfrac{100}{2}$ = ₹50

New profit = ₹150 - ₹50 = ₹100

New profit percentage = $\dfrac{100}{50} \times 100$% = 200%

As 200% ≠ 2 x 50%, the profit percentage does not double.

So, Statement II is false.

Hence, option 4 is the correct option.

Statement I: If the list price of an item is ₹950 and 6% GST is charged on it, then the SP of the item is ₹1,007.

Statement II: SP = list price + taxes

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

List price of the item = ₹950 and rate of GST = 6%

GST = 6% of ₹950

$= \dfrac{6}{100} \times 950 \\[1em] = \dfrac{5700}{100} \\[1em] = ₹57$

S.P. of the item = List price + GST

= ₹950 + ₹57

= ₹1,007

So, Statement I is true.

GST is calculated on the selling price of an item and is added to the bill, so S.P. = list price + taxes.

So, Statement II is true.

Hence, option 3 is the correct option.