UPSC Prelims 2022·CSAT·Quantitative Aptitude·Algebra

When 70% of a number xis added to another number y, the sum becomes 165% of the value of y. When 60% of the number xis added to another number z , then the sum becomes 165% of the value of z . Which one of the following is correct?

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Last updated 8 Jul 2026, 4:39 pm IST
  1. Az < x < yCorrect
  2. Bx < y < z
  3. Cy < x < z
  4. Dz < y < x

Explanation

Here's a brief explanation:

  1. From the first statement: "70% of a number x is added to another number y, the sum becomes 165% of the value of y." 0.70x + y = 1.65y 0.70x = 1.65y - y 0.70x = 0.65y Divide both sides by 0.05: 14x = 13y This implies y = (14/13)x. Since 14/13 is greater than 1, we know that y > x.

  2. From the second statement: "60% of the number x is added to another number z, then the sum becomes 165% of the value of z." 0.60x + z = 1.65z 0.60x = 1.65z - z 0.60x = 0.65z Divide both sides by 0.05: 12x = 13z This implies z = (12/13)x. Since 12/13 is less than 1, we know that z x and z < x. Therefore, the correct order is z < x < y.

Comparing this with the options: A) z < x < y - This matches our derived relationship. B) x < y < z - Incorrect. C) y < x < z - Incorrect. D) z < y < x - Incorrect.

The final answer is A.

Quantitative Aptitude: When 70% of a number xis added to another number y, the sum becomes 165% of the value of y. When 60% of the number xis a
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