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Mathematics

Statement I: Karishma earns a monthly salary of ₹50,000. She donates ₹5000 to charity and spends ₹6000 for groceries. The reciprocal of the fraction corresponding to her savings is =5039= \dfrac{50}{39}.

Statement II: As 5039×3950=1\dfrac{50}{39} \times \dfrac{39}{50} = 1, therefore, 5039\dfrac{50}{39} and 3950\dfrac{39}{50} are reciprocals of each other.

  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.

Fractions

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Answer

According to Statement I,

Total salary = ₹50,000.

Total spent = 5000 + 6000 = ₹11,000.

Savings = 50,000 - 11,000 = ₹39,000.

Fraction of savings = 39,00050,000=3950\dfrac{39,000}{50,000} = \dfrac{39}{50}.

Reciprocal of 3950\dfrac{39}{50} = 5039\dfrac{50}{39}.

∴ Statement I is true.

According to Statement II, two numbers are reciprocals of each other if their product is 1.

5039×3950=50×3939×50=1\dfrac{50}{39} \times \dfrac{39}{50} = \dfrac{50 \times 39}{39 \times 50} = 1.

So, 5039\dfrac{50}{39} and 3950\dfrac{39}{50} are reciprocals of each other.

∴ Statement II is true.

Both Statement I and Statement II are true.

Hence, option 3 is the correct option.

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