Get the Knowledge that sets you free...
Science & Math for K6 - K12 Students

Exercises - XIII,XIV &XV
Exercise-XIII
1. The average weight of 10 oarsmen in a boat is increased by 1.5 pounds when one of the crew, who weighs 58 pounds is replaced by a new man. Find the weight of new man ?
 Sol: Total weight increased = 10 × 1.5 pounds = 15 pounds weight of new man = (58 + 15) pounds = 73 pounds

2. 10 sheep and 5 pigs were bought for \$ 6000. If the average price of a sheep be \$ 450, find the average price of a pig
 Sol: Total price of 10 sheep = 10 × 450 = \$ 4500 Total price of 5 pigs = \$ 6000 – \$ 4500 = \$ 1500 Average price of a pig = = \$ 300

3. of x is 900 what is the value of of x ?
 Sol: × x = 900 x = 2400 of 2400

4. x, y are natural numbers if x2 + y2 = 80 and (x – y)2 = 36, what is the value of xy ?
 Sol: x2 + y2 – 2xy = (x – y)2 80 – 2xy = 36 80 – 36 = 2xy 2xy = 44 xy = 22

5. If 1 is added to the denominator of a fraction the fraction becomes . If 1 is added to the numerator, the fraction becomes 1 what is the fraction
 Sol: = 2x = y + 1 2x – y = 1 ––– (1) = 1 x + 1 = y x – y = – 1 ––– (2) subtract 2 from 1 x + 1 = y 2 + 1 = y y = 3 =

6. The sum of three numbers is 132. If the first number be twice the second and third number be one third of the first, then the second number is
 Sol: Let 2nd number be x 1st number be 2x 3rd number be × 2x = 132 = 132 11x = 132 × 3 2nd number = x = 36

7. If a + b = 45, b + c = 55, c + 3a = 90 what is the value of the third number ?
 Sol: a + 10 = c ––– (3) c + 3a = 90 ––– (4) c = 90 – 3a c = 10 + a 90 – 3a = 10 + a 90 – 10 = 3a + a 4a = 80 a = 20 c = 10 + a = 10 + 20 c = 30

8. A circular wire of radius 42" is cut and bent in the form of a rectangle whose sides are in the ratio 6 : 5. The smaller side of the rectangle is
 Sol: circumference of circle = perimeter of rectangle 2πR = 2(L + B) L : B = 6 : 5 Let L = 6x, B = 5x 264 = 22x x = 12 B = 5x = 5 × 12 = 60"

9. The number of rounds that a wheel of diameter m will make in going 4 km (1 km = 1000 metres)
 Sol: Number of rounds = = = = 2000

10.
The area of the circle inscribed in an equilateral triangle is 462 sqinches. The sides of the triangle is
 Sol: πr2 = 462 r2 = 147 r = = r = 7√3 radius of incircle = × height of triangle 7√3 = × height of the triangle height of the triangle = 21√3 height of triangle = side = side side = 42"

11. a, b, c, d are four numbers such that a – s = b + 6 = c + 9 = d – 1. What is the value of a – d : b – c
 Sol: a – 5 = d – 1 a – d = 5 – 1 a – d = 4 b + 6 = c + 9 b – c = 9 – 6 b – c = 3 a – d : b – c = 4 : 3

12. a > b, b < c, c > d If a = b + 2, b = c – 3, c = d + 4 what is the value of (a – d)2 + (a – d)
 Sol: a = b + 2 b = c – 3 a = c – 3 + 2 a = c – 1 a = d + 4 – 1 a = d + 3 a – d = 3 (a – d)2 + (a – d) = (3)2 + 3 = 12

13.
The perimeter of rectangle is 64" and the length is 18". What is the area of ΔPOQ ?
 Sol: 2(L + B) = 64" 2(18" + B) = 64" (18" + B) = 32" QR = B = 14" OX = × QR = × 14" = 7" Area of ΔPOQ = × QP × OX = 63" sqinches

Physics Chemistry Biology Math
 Mechanics Thermal Physics Waves & Optics
 Electricity &Magnetism Electromagnetism Atomic and Nuclear Physics
 Structure of Matter States of Matter Chemical Reactions
 Metals & Non-metals Organic Chemistry
 Biochemistry & Cell Biology Genetics Evolutionary Biology
 Plant Form & Function Animal Form & Function Human Physiology
 Arithmetic Algebra Geometry
 Calculus Statistics