# Case based: 2

### The school Principal wants to address the students of classes eighth to tenth on the importance of personal hygiene. He asks the teacher in charge of the school to arrange all the students of eighth, ninth and tenth classes in a single hall. There are 84 students from eighth class, 63 students from ninth and 42 students from tenth class.

Class 10 Case based problem of Chapter 1 Real Number 1

Class 10 Case based problem of Chapter 1 Real Number 2

(A) What is the minimum number of rows in which the students can be seated such that students belonging to the same class are seated in the same row ?

(a) 7                         (b) 9

(c) 21                        (d) 42

(B) Realizing that the hall can accommodates more students, the school Principal now wants to include 98 students of class seventh also. What will be the number of students and minimum number of rows such that students belonging to the same class are seated in the same row ? (C) Suppose the bus incharge of the school has to arrange busses in the morning for a picnic. There are two lines of busses, line A and line B. Busses on line A leave after every 15 minutes while busses on line B leave after every 20 minutes. In a day, how many times do busses on both lines A and B leave together between 8 a.m. and 11 a.m., if firstly, busses leave together at 8 a.m. ?

(a) 3                           (b) 4

(c) 5                            (d) 6

(D) Three numbers in the ratio of 3:4:5 and their LCM is 2400. The HCF of the number is :

(a) 40                         (b) 60

(c) 80                         (d) 120

(E) The product of two numbers is 2028 and their HCF is 13. The LCM of the number is:

(a) 13                           (b) 156

(c) 2028                       (d) 26364

Solution: (A) Answer is (b) 9

#### Explanation:

As we have to find the minimum number of rows, we have to first take the HCF of 84, 63 and 42

84 =  2²×3×7

63 = 3²×7

42 = 2×3×7 HCF = 3×7 = 21

So, 21 students of each class can be seated in one row. That means there will be 4 rows for class eighth, 3 rows for class ninth and 2 rows for class tenth.

Total number of rows = 4 + 3 +2 = 9

(B) Answer (d) Number of students of same class in one row = 7, minimum number of rows = 41

#### Explanation:

We will now calculate the HCF of 42, 63, 84 and 98.

42 = 2×3×7

63 = 3²×7

84 = 2²×3×7

98 = 2×7² HCF = 7

So, 7 students of each class can now be seated in one row. That means there will be 12 rows for class eighth, 9 rows for class ninth, 6 rows for class tenth and 14 rows for class seventh.

Total number of rows = 12 + 9 + 6 + 14 = 41

#### Explanation:

Buses on line A leave after every 15 minutes

Buses on line B leave after every 20 minutes

15 = 3 × 5

20 = 2 × 2 × 5

LCM of these two numbers = 2 × 2 × 3 × 5

= 60 minutes

Busese on both the lines a and B leave together in every = 60 minutes

Hence, they leave together = 8 a.m., 9 a.m. 10 a.m. and 11 a.m.

4 times from 8 a.m. to 11 a.m.

#### Explanation:

Let the number be 3x, 4x and 5x.

Their LCM = 3 ×4 × 5 × x

⇒  60x = 2400

⇒ x = 40

Thus the numbers are 120, 160 and 200.

To find their HCF, we find their prime factors:

120 = 2 × 2 × 2 × 3 × 5

160 = 2 × 2 × 2 × 2 × 2 ×5

200 = 2 × 2 × 2 × 5 × 5

HCF = 2 × 2 × 2 × 5 = 40

#### Eplanation:

The product of two numbers  = 2028

HCF of two numbers = 13

Using formula

Product of two numbers = HCF of two numbers × LCM of two numbers

⇒ 2028 = 13 × LCM of two numbers Then LCM of two numbers = 156

## Some others Case study

Class 10 Case based problem of Chapter 1 Real Number 1

Class 10 Case based problem of Chapter 1 Real Number 2

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