Practice 1.5, Algebra, ssc,

1. Two numbers differ by 3. The sum of twice the smaller number and thrice the greater number is 19. Find the numbers.

Solution

Let the smaller number be x and the larger number be y. 
Given that the two numbers differ by 3 so,
y−x=3                                               …..(I)
Also, sum of twice the smaller number and thrice the greater number is 19
So, 
2x+3y=19                                 ……(II)
The two equations obtained are 
y−x=3 
2x+3y=19
Multiplying (I) by 2 we get

2y−2x=6                     …..(III)
Adding (III) and (II) we have
5y = 25
⇒y=25/5 =5
Putting the value of y = 5 in (I) we get
5−x=3
⇒−x=3−5
⇒−x=−2
⇒x=2
Thus, the two numbers are 2 and 5.

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