Aptitude Day 37

Answers of Day 36:      1. 120

                                       2. 4

      

1. Of two numbers, 3 times the smaller one is less than 4 times the larger one by 6. If the twice of the sum of their number is larger than their difference by 4. What are the two numbers?

Solution:

                 Let the numbers be x and y.

                 Considering, x is greater than y.

                 4x-3y=6     [condition 1] --------- Equation 1

                 2(x + y)-(x - y) = 4    [condition 2]

                 Condition 2 becomes,

                        x+3y = 4   --------Equation 2

                 By solving Equation 1 and 2, we get

                           x=2 and y= 2/3.

                 These are the 2 numbers.

2. A fraction becomes 1/3 when 1 is subtracted from both its numerator and denominator and it becomes 1/2 when 1 is added to both the numerator and denominator, find the fraction.

Solution:

                 Let the fraction be x/y.

                (x - 1)/(y - 1) = 1/3     [condition 1]

                3(x-1) = y-1

                3x-y=2 ------------ Equation 1

                (x+1)/(y+1) = 1/2

                2(x+1) = y+1

                2x-y= -1 ---------- Equation 2

                 

                By solving equation 1 and 2, we get

                         x=3 and y=7.

                Hence, the fraction is 3/7.