KnowledgeBoat Logo
|

Mathematics

Assertion (A) : If we decrease ₹ 120 by 1212%12\dfrac{1}{2}\%, then decreased amount = ₹ 105.

Reason (R) : Percentage change = (Actual change (increase/decrease)Original quantity×100)%\Big(\dfrac{\text{Actual change (increase/decrease)}}{\text{Original quantity}} \times 100\Big)\%.

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. A is true, but R is false.

  4. A is false, but R is true.

Percent & Percentage

2 Likes

Answer

⇒1212% of ₹ 120⇒252100×120⇒25200×120⇒25×35⇒5×3⇒15.\Rightarrow 12\dfrac{1}{2}\% \text{ of ₹ }120 \\[1em] \Rightarrow \dfrac{\dfrac{25}{2}}{100} \times 120 \\[1em] \Rightarrow \dfrac{25}{200} \times 120 \\[1em] \Rightarrow \dfrac{25 \times 3}{5} \\[1em] \Rightarrow 5 \times 3 \\[1em] \Rightarrow 15.

Decreased amount = ₹ 120 - ₹ 15 = ₹ 105

So, assertion (A) is true.

Percentage change = (Actual change (increase/decrease)Original quantity×100)%\Big(\dfrac{\text{Actual change (increase/decrease)}}{\text{Original quantity}} \times 100\Big)\%

If a quantity changes by 15 out of 120, then:

Percentage change =(15120×100)%=15012%=12.5%\text{Percentage change } = \Big(\dfrac{15}{120} \times 100\Big)\%\\[1em] = \dfrac{150}{12}\%\\[1em] = 12.5\%\\[1em]

So, reason (R) is true and reason clearly explains assertion.

Hence, option 1 is the correct option.

Answered By

1 Like

Related Questions