Skip to main content

Aptitude Day 35


Problems on Numbers

1. The sum of the 2 numbers is 13 and the sum of their squares is 85. Find the numbers. 

Solution:
                  Let the numbers be x and (13-x).
                            x2+(13-x)2=85    [Given condition] 
                            x2+169-26x+x2=85
                            2x2-26x+84=0
                             x2-13x+42=0
                             x2-7x-6x+42=0
                             x(x-7)-6(x-7)=0
                              (x-7)(x-6)=0
                                  x=7, 6.
                  The two numbers are 7 and 6.           

2. If the sum of the two numbers is 22 and their product is 40. Find the difference between the 2 numbers.

Solution:
                 Let the numbers be x and y.
                  x+y = 22 and xy = 40 [Given]
                  (x-y)2= (x+y)2 – 4xy    [Since (x+y)– 4xy = x2+2xy+y2-4xy  = x2-2xy+y2]  
                           = (22)2-4(40)
                           =484-160
                  (x-y)2= 324
                     x-y = 18
         

                    


Comments

Popular posts from this blog

Aptitude Day 59

Answers of Day 58:     1. 1/90.     2. 20 Problems to solve: 1. The product of two numbers is 33 and the sum of their squares is 130. Find their difference. 2. The sum of two numbers is 100 and their difference is 20. Find their product.

Vocabulary Day 55

Dilemma Thesaurus: Noun : problem            double bind, difficulty, crisis, embarrassment, mess, puzzle...  Antonyms :  solution...  Example sentences:                  That's a serious dilemma we should think about that.          He'll never share his dilemma with anyone. 

Aptitude Day 55

Problems On Numbers 1. The difference between the squares of two numbers is 28000 and the sum of their numbers is 400. Find the numbers. Solution:                 Let the 2 numbers be x and y.                 (x 2 -y 2 ) / (x+y) = 28000/400                 (x+y)(x-y) / (x+y) =  70                 x-y = 70 ------ Equation 1                 x+y = 400 ---- Equation 2                 By solving equations 1 and 2 we get,                 x = 235 and y = 165.                 The numbers are 235 and 165. 2. The sum of three consecutive numbers is 315. The middle number is: Solution:                 Let t...