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Two no. Are in the ratio3:4. The difference between their squares is 28. Find the greatest no.?
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Two no. Are in the ratio3:4. The difference between their squares is 2...
Problem Statement

We are given two numbers in the ratio of 3:4. The difference between their squares is 28. We need to find the greatest number.


Solution

Let us assume the two numbers to be 3x and 4x. As per the question, the difference between their squares is 28. Therefore, we can write:


(4x)2 - (3x)2 = 28


Simplifying the above equation, we get:


16x2 - 9x2 = 28


7x2 = 28


x2 = 4


x = 2 (as x cannot be negative)


Therefore, the two numbers are:


3x = 6 and 4x = 8


The greatest number is 8.


Answer

The greatest number is 8.
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Two no. Are in the ratio3:4. The difference between their squares is 2...
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Two no. Are in the ratio3:4. The difference between their squares is 28. Find the greatest no.?
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