RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 10. Quadratic Equations

Subject: Maths - Class 10th

Q. No. 39 of Exercise 10E

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39

The sum of the reciprocals of Meena's ages (in years) 3 years ago and 5 years hence is 1/3. Find her present age.

Let the present age of Meena be x years

Meena’s age three years ago = (x – 3) years


Meena’s age five years hence = (x + 5) years


According to given question





x2 + 2x – 15 = 6x + 6


x2 – 4x – 21 = 0


Using the splitting middle term – the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 1 b = – 4 c = – 21


= 1. – 21 = – 21


And either of their sum or difference = b


= – 4


Thus the two terms are – 7 and 3


Sum = – 7 + 3 = – 4


Product = – 7.3 = – 21


x2 – 7x + 3x – 21 = 0


x (x – 7) + 3(x – 7) = 0


(x – 7) (x + 3) = 0


x = – 3 or x = 7


x = 7 age cannot be negative


Hence the present age of Meena is 7 years


Chapter Exercises

Exercise 10A
Exercise 10B
Exercise 10C
Exercise 10D
Exercise 10E
Exercise 10F

More Exercise Questions

1

The sum of a natural number and its square is 156. Find the number.
2

The sum of a natural number and its positive square root is 132. Find the number.
3

The sum of two natural numbers is 28 and their product is 192. Find the numbers.
4

The sum of the squares of two consecutive positive integers is 365. Find the integers.
5

The sum of the squares of two consecutive positive odd numbers is 514. Find the numbers.
6

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7

The product of two consecutive positive integers is 306. Find the integers.
8

Two natural numbers differ by 3 and their product is 504. Find the numbers.
9

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10

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11

Find two consecutive positive even integers whose product is 288.
12

The sum of two natural numbers is 9 and the sum of their reciprocals is 1/2. Find the numbers.
13

The sum of two natural numbers is 15 and the sum of their reciprocals is 3/10. Find the numbers.
14

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15

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16

The sum of the squares of two consecutive multiples of 7 is 1225. Find the multiples.
17

The sum of a natural number and its reciprocal is 65/8. Find the number.
18

Divide 57 into two parts whose product is 680.
19

Divide 27 into two parts such that the sum of their reciprocals is 3/20.
20

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21

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22

The difference of the squares of two natural numbers is 45. The square of the smaller number is four times the larger number. Find the numbers.
23

Three consecutive positive integers are such that the sum of the square of the first and the product of the other two is 46. Find the integers.
24

A two – digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.
25

A two – digit number is such that the product of its digits is 14. If 45 is added to the number, the digits interchange their places. Find the number.
26

The denominator of a fraction is 3 more than its numerator. The sum of the fraction and its reciprocal is . Find the fraction.
27

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28

The sum of a number and its reciprocal is . Find the number.
29

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30

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31

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32

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33

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34

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35

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36

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37

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38

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39

The sum of the reciprocals of Meena's ages (in years) 3 years ago and 5 years hence is 1/3. Find her present age.
40

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41

The product of Tanvy's age (in years) 5 years ago and her age 8 years later is 30. Find her present age.
42

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43

A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, find the first speed of the truck.
44

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45

A train covers a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less then it would have taken 3 hours more to cover the same distance. Find the usual speed of the train.
46

A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/hr more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?
47

A train travels 180 km at a uniform speed. If the speed had been 9 km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.
48

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49

A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. Find its usual speed.
50

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51

A motor boat whose speed in still water is 18 km/hr, takes 1 hour more to go 24 km upstream than to return to the same spot. Find the speed of the stream.
52

The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.
53

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54

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55

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56

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57

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58

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59

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60

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61

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62

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63

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64

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65

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66

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67

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68

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69

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70

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71

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