QUESTION

CSAT

Medium

Maths

Prelims 2022

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?

Select an option to attempt

Explanation

To simplify, let's express the percentages in decimal form:

Given:

  1. 0.7x+y=1.65y0.7x + y = 1.65y

Rearranging: 0.7x=0.65y0.7x = 0.65y

Dividing both sides by yy: xy=0.650.7\frac{x}{y} = \frac{0.65}{0.7} Since 0.650.7<1\frac{0.65}{0.7} < 1, we have x<yx < y. …(i)

  1. 0.6x+z=1.65z0.6x + z = 1.65z

Rearranging: 0.6x=0.65z0.6x = 0.65z

Dividing both sides by zz: xz=0.650.6\frac{x}{z} = \frac{0.65}{0.6}

Since 0.650.6>1\frac{0.65}{0.6} > 1, we have x>zx > z. …(ii)

Combining (i) and (ii), we get: z<x<yz < x < y

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