Question

The sum of two numbers is 35. Four times the larger number is 5 more than 5 times the smaller number. Find these numbers.

Answer 1

Answer :

Let us take the two numbers as x and y with x > y

By the given conditions,

x + y = 35 ...(i)

4x = 5y + 5

or, 4 (35 - y) = 5y + 5, by (i)

or, 140 - 4y = 5y + 5

or, 9y = 135

or, y = 15

Putting y = 15 in (i), we get

x + 15 = 35

or, x = 35 - 15

or, x = 20

Therefore, the two numbers are 20 and 15.

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Answer 2

Solution :

Let x , ( 35 - x ) are two numbers.

According to the problem given ,

4 times the larger number = 5 more

than 5 times of the smaller number

=> 4x = 5( 35 - x ) + 5

=> 4x = 175 - 5x + 5

=> 4x + 5x = 180

=> 9x = 180

=> x = 180/9

=> x = 20

Therefore ,

Required two numbers are,

First number = x = 20,

Second number = 35 - x = 35 - 20 = 15

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