When 70% of a number x is added to another number y, the sum becomes 165% of the value of y. When 60% of the number x is added to another number z, then the sum becomes 165% of the value of z. Which one of the following is correct ?
- A.z < x < y
- B.x < y < z
- C.y < x < z
- D.z < y < x
▶ Answer & Explanation
Correct answer: A. z < x < y
The first condition translates to 0.7x + y = 1.65y, which simplifies to 0.7x = 0.65y, or x = (0.65/0.7)y. The second condition translates to 0.6x + z = 1.65z, which simplifies to 0.6x = 0.65z, or x = (0.65/0.6)z. Since (0.65/0.7) < (0.65/0.6), it follows that x/y < x/z. As x is positive, this implies y > z. Also, comparing x = (0.65/0.7)y and x = (0.65/0.6)z, we can infer the relationship between x, y, and z. Substituting the expression for x from the first equation into the second gives (0.65/0.7)y = (0.65/0.6)z, which simplifies to y/0.7 = z/0.6, or y = (0.7/0.6)z. Since 0.7/0.6 > 1, we have y > z. From 0.7x = 0.65y, we get x = (0.65/0.7)y, so x < y. From 0.6x = 0.65z, we get x = (0.65/0.6)z, so x > z. Combining these, we get z < x < y.
Source: UPSC csat 2022