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Practice 1.5, Algebra, ssc,

21 Dec 2020 10:12 pm

  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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