IMO Level 1 Mathematics Olympiad (SOF) Class 10: Questions 84  89 of 968
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Question number: 84
» Pair of Linear Equations in Two Variables
Question
Places and are 120 km apart from each other on a national highway. A car starts from and another from at the same time. If they go in the same direction then they meet in 6 hours and if they go in opposite directions they meet in hours. The speeds of the cars are ________
Choices
Choice (4)  Response  

a. 
 
b. 
 
c. 
 
d. 

Question number: 85
» Pair of Linear Equations in Two Variables
Question
The digit at the ten’s place of a two digit number is twice the digit at the unit’s place. If the sum of this number and the number formed by reversing the digits is 99, find the number.
Choices
Choice (4)  Response  

a.  24  
b.  52  
c.  36  
d.  63 
Question number: 86
Question
If are the roots of then is ________
Choices
Choice (4)  Response  

a.  15  
b.  20  
c.  10  
d.  5 
Question number: 87
» Pair of Linear Equations in Two Variables
Question
The ratio between a two – digit number and the sum of digits of that number is . If the digit in the unit place is 3 more than the digit in the tenth place, what is the number?
Choices
Choice (4)  Response  

a.  40  
b.  63  
c.  24  
d.  36 
Question number: 88
» Pair of Linear Equations in Two Variables
Question
The value of k for which the system of equations has no solution, is ________
Choices
Choice (4)  Response  

a.  1  
b.  10  
c.  6  
d.  3 
Question number: 89
Question
If one zero of the polynomial is a reciprocal of the other, then k is equal to ________
Choices
Choice (4)  Response  

a.  5  
b.  7  
c.  9  
d.  2 