RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 10. Quadratic Equations

Subject: Maths - Class 10th

Q. No. 38 of Exercise 10E

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38

One year ago, a man was 8 times as old as his son. Now, his age is equal to the square of his son's age. Find their present ages.

Let the present age of son be x years

The present age of man = x2 years


One year ago age of son = (x – 1)years


age of man = (x2 – 1)years


According to given question


x2 – 1 = 8(x – 1)


x2 – 1 = 8x – 8


x2 – 8x + 7 = 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 = – 8 c = 7


= 1.7 = 7


And either of their sum or difference = b


= – 8


Thus the two terms are – 7 and – 1


Sum = – 7 – 1 = – 8


Product = – 7. – 1 = 7


x2 – 7x – x + 7 = 0


x(x – 7) – 1(x – 7) = 0


(x – 7) (x – 1) = 0


x = 1 or x = 7


Man’s age cannot be 1 year


Thus x = 7


Thus the present age of son is 7years


The present age of man is 72 = 49years


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

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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

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9

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10

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11

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

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13

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14

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15

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16

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17

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18

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19

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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

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24

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

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26

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27

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28

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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

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40

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41

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42

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43

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44

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45

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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

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48

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49

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50

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51

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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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