d Question 29 & 30 Sum of squares of three numbers is 138. Sum of their products with each other is 131. Find the sum of numbers. Two candidates contested an election .7500 votes were cast in an election. Out of these 20% were invalid. 55% votes were scored by one candidate. Find the number of votes scored by each candidate. | Job Exam Rare Mathematics (JEMrare) - Solved MCQs

# Question 29 & 30 Sum of squares of three numbers is 138. Sum of their products with each other is 131. Find the sum of numbers. Two candidates contested an election .7500 votes were cast in an election. Out of these 20% were invalid. 55% votes were scored by one candidate. Find the number of votes scored by each candidate.

Question 29 & 30 Sum of squares of three numbers is 138. Sum of their products with each other is 131. Find the sum of numbers.

Solution

Let the numbers be ‘x’, ‘y’ and ‘z’;

According to first condition sum of squares is 138;

According to 2nd condition, sum of products of two numbers taken  at a time is  equal to 131, so;

To solve this we take sum of numbers and then take square of their algebraic sum!

Put values from eq (1) and (2) in eq (3);

Taking square root on both sides;

rounding off

so, Their sum is 20

Question 30 : Two candidates contested an election .7500 votes were cast in an election. Out of these 20% were invalid. 55% votes were scored by one candidate. Find the number of votes scored by each candidate.

Solution:

Here,

So,

So, Valid Votes by 2nd candidate were 2700