# IMO Level 1- Mathematics Olympiad (SOF) Class 10: Questions 84 - 89 of 968

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## Question number: 84

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MCQ▾

### 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

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MCQ▾

### 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

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MCQ▾

### Question

If are the roots of then is ________

### Choices

Choice (4)Response

a.

-15

b.

-20

c.

-10

d.

-5

## Question number: 87

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MCQ▾

### 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

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MCQ▾

### 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

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MCQ▾

### 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

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