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Science & Math for K6 - K12 Students

Exercises - XIX,XX &XXI
Exercise-XIX
1.
 Sol:

2. If (a, b) and (a + 3 , b + m) are two points on the line defined by the equation x = 3y – 7 then m =
 Sol: x = 3y – 7 put x = a , y = b , x = a + 3 , y = b + m a = 3b – 7 a – 3b = – 7 x = a + 3 , y = b + 4 a + 3 = 3(b + m) – 7 a + 3 = 3b + 3m – 7 a – 3b = 3m – 10 (bu t a – 3b = – 7) – 7 = 3m – 10 3m = 10 – 7 3m = 3 m = 1

3. If David loses 8 pounds, he will weigh twice as much as his sister. Together they now weigh 198 pounds. What is David's present weight in pounds ?
 Sol: Let David's weight be x pounds David's present weight = x – 8 pounds sister weight = (x – 8) pounds x – 8 + (x – 8) = 198 2(x – 8) + 1(x – 8) = 198 × 2 2x – 16 + x – 8 = 396 3x = 420 x = 140 Present weight of David = (140 – 8) = 132 pounds

4. The cost of 12 maps and 10 books is \$38 and the cost of 20 maps and 15 books is \$ 60. What is the difference between the prices of each item ?
 Sol: Let cost of a map be \$ x Let cost of a book be \$ y 12x + 10y = 38 12 × 1.50 + 10y = 38 18 + 10y = 38 10y = 20 y = 2 y – x = \$ 2 – \$ 1.50 = \$ 0.50

5. A supermarket's total sales for the month of February of this year was \$ 384. If the total sales for the same month last year was \$ 320 million. What was the percent increase in sales ?
 Sol: Increase in sales = \$ 384 – \$ 320 = \$ 64 % increase = = 20 %

6. List I : 3 , 6 , 8 , 19
List II : x , 3 , 6 , 8 , 19
If the median of the List I is equal to the median of the numbers in List II , what is the value of x ?
 Sol: The median of List I is = 7 The median of List II is also 7 The median of x , 3 , 6 , 8 , 19 is 7 As the median of list II is 7 3 , 6 , x , 8 , 19 are the numbers x = 7

7. The present ratio of students to teachers in a school is 30. If 50 new students and 5 new teachers join the ratio of students to teachers would then be 25 : 1. What is the present number of students?
 Sol: Let the number of students : teachers = 30 x : 1x 30x + 50 : x + 5 = 25 : 1 (30x + 50) = 25(x + 5) 30x + 50 = 25x + 125 5x = 75 x = 15 Number of students = 30 × 15 + 50 = 500

8. What is the smallest integer n for which 25n > 512
 Sol: (52)n > 512 (52)6 512 (52)7 > 512 514 > 512 smallest integer n = 7

9. If 784 = 2a × 7b then the value of 5a + 6b =
 Sol: 784 = 28 × 28 = 7 × 4 × 7 × 4 = 72 × 42 2a × 7b = 72 × 24 a = 4 b = 2 5a + 6b = 5 × 4 + 6 × 2 = 32

10. If p is the product of the integers from 1 to 20, inclusive what is the greatest integer k for which 5k is a factor of p ?
 Sol: 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10 × 11 × 12 × 13 × 14 × 15 × 16 × 17 × 18 × 19 × 20 Product of multiples of 3 = 3 × 6 × 9 × 12 × 15 × 18 = 3 × 3 × 2 × 3 × 3 × 3 × 4 × 3 × 5 × 3 × 3 × 2 = 38 × 2 × 4 ×5 × 2 Greatest integer = 38 k = 8

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