Easy and detail solution of RS Aggarwal Class 8 Chapter 8 Exercise 8b Solution (Linear Equations). All solution are provided in detail, therefore each and every student can understand solution easily.
RS Aggarwal Class 8 Exercise 8b Solution
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(1) Two numbers are in the ratio 8 : 3. If the sum of the numbers is 143, find the numbers.
Solution:
Let the number is 8x and 3x then according to question,
⇒8x + 3x = 143
⇒11x =143 i.e. x = 13
Therefore number is 8x = 104
and 3x = 39
Hence, number is 104 and 39
(2) 2/3 of a number is 20 less than the original number.Find the number.
(3) Four – fifths of a number is 10 more than two – thirds of the number.
Find the number.
(4) Twenty – four is divided into two parts such that 7 times the first part added to 5 – times the second part makes 146. Find each part.
(5) Find the number whose fifth part increased by 5 is equal to its fourth part diminished by 5.
(6) Three numbers are in the ratio 4 : 5: 6 . If the sum of the largest and the smallest equals the sum of the third and 55. Find the numbers.
(7) If 10 be added to four times a certain number, the result is 5 less than five times the number. Find the number.
Solution:
Let the number is x then according to the question,
⇒ 4x+10 = 5x-5
⇒ 4x-5x = -5-10
⇒ -x = -15 i.e.x=15
(8) Two numbers are such that the ratio between then 3 : 5. If each is increased by 10. The ratio between the new numbers so formed is 5 : 7. Find the original numbers.
(9) Find three consecutive odd numbers whose sum is 147.
(10) Find three consecutive even numbers whose sum is 234.
(11) The sum of the digits of a two – digit number is 12.
If the new number formed by reversing the digits is greater than the original number by 54. Find the original number. Check your solution.
(12) The digit in the tens place of a two – digit number is three times that in the units place. If the digits are reversed, the new number will be 36 less than the original number.
Find the original number. Check your solution.
(13) The denominator of a rational number is greater than its numerator by 7. If the numerator is increased by 17 and the denominator decreased by 6, the new number becomes 2. Find the original number.
(14) In a fraction, twice the numerator is 2 more than the denominator.
If 3 is added to the numerator and to the denominator, the new fraction is 2/3 . Find the original fraction.
(15) The length of a rectangle exceeds its breadth by 7 cm. If the length is decreased by 4 cm and the breadth is increased by 3 cm, the area of the new rectangle is the same as the area of the original rectangle.
Find the length and the breadth of the original rectangle.
(16) The width of a rectangle is two – thirds its length. If the perimeter is 180 metres,
find the dimensions of the rectangle.
(18) Two angles of a triangle are in the ratio 4 : 5 . If the sum of these angles is equal to the third angle. Find the angles of the triangle.
(19) A steamer goes downstream from one port to another in 9 hours. It covers the same distance upstream in 10 hours. If the speed of the stream be 1 km/h.
Find the speed of the steamer in still water and water and the distance between the ports.
(20) The distance between two stations is 300 km. Two motorcyclists start simultaneously from these stations and move towards each other. The speed of one of them is 7 km/h more than that of the other.
If the distance between them after 2 hours of their start is 34 km. Find the speed of each motorcyclist. Check your solution.
(21) Divide 150 into three parts such that the second number is five – sixths the first and third number is four – fifths the second.
(22) Divide 4500 into two parts such that 5% of the first part is equal to 10% of the second part.
(23) Rakhi’s mother is four times as old as Rakhi. After 5 years, her mother will be three times as old as she will be then.Find their present ages.
(24) Monu’s father is 26 years younger than Monu’s grand- father and 29 years older than Monu. The sum of the ages of all the three is 135 years.
What is the age of each one of them?
(25) A man is 10 times older than his grandson.
He is also 54 years older than him. Find their present ages.
Solution:
Let his grandson’s age is x years
Then age of Man is 10x years and also his age will be (x + 54) years
Now, both age of Man will be equal,
⇒10x = x + 54
⇒9x = 54 i.e x = 6
Therefore Grandson’s age = 6 years
and Man’s age = 10x = 60 years
(26) The difference between the ages of two cousins is 10 years, 15 years ago, If the elder one was twice as old as the younger one; find their present ages.
Solution:
Let the present ages of both are x and y .
And x is elder and y is younger.
⇒ x – y = 10 ……..(i)
Then,
15 years ago their ages are (x – 15)years and (y – 15) years
According to question, (x – 15) = 2 (y – 15)
⇒ x – 15 = 2y – 30
⇒ 2y – x = 30 – 15 = 15
⇒ 2y – x =15 …….(ii)
From Eq. (i) and (ii) , we get
⇒ x = 35 and y = 25
Hence the ages of both cousins are 35 years and 25 years.
(27) Half on a herd of deer are grazing in the field and three- fourths of the remaining are playing nearby.
The rest 9 are drinking water from the pond. Find the number of deer in the herd.
