Rs Aggarwal Solutions: Exercise 1G - Rational Numbers | Mathematics (Maths) Class 8 PDF Download

Q.1. From a rope 11 m long, two pieces of lengths are cut off. What is the length of the remaining rope?
Ans.
Length of the rope when two pieces of lengths are cut off = Total length of the rope - Length of the two cut off pieces

Now,


LCM of 5 and 10 is 10, i.e.,(5 × 1 × 2)
We have:


Length of the remaining rope =

Therefore, the length of the remaining rope is

Q.2. A drum full of rice weighs If the empty drum weighs  find the weight of rice in the drum.
Ans.
Weight of rice in the drum = Weight of the drum full of rice - Weight of the empty drum


Therefore, the weight of rice in the drum is

Q.3. A basket contains three types of fruits weighing in all. Ifof these be apples,  be oranges and the rest pears, what is the weight of the pears in the basket?
Ans.
Weight of pears in the basket = Weight of the basket containing three types of fruits - (Weight of apples + Weight of oranges)

Now,

LCM of 9 and 6 is 18, that is, (3 × 3 × 2).

We have:


Now,
Weight of pears in the basket =

Therefore, the weight of the pears in the basket is

Q.4. On one day a rickshaw puller earned Rs 160. Out of his earnings he spent Rson tea and snacks, Rson food and Rs on repairs of the rickshaw. How much did he save on that day?
Ans.
Total earning = Rs. 160

Money spent on tea and snacks =  
Money spent on food =  
Money spent on repairs = 

Let the savings be Rs.x.

Money spent on tea and snacks + Money spent on food + Money spent on repairs + Savings = Total earning


Rs.
So, the savings are Rs.

Q.5. Find the cost of  metres of cloth at Rs  per metre.
Ans. Cost of 1 m of cloth =
So, cost of m of cloth

So, the cost ofm of cloth is

Q.6. A car is moving at an average speed of km/hr. How much distance will it cover in hours?
Ans.
Speed = km/h 6025 km/h
Time =
We know that

⇒ Speed × Time = Distance

Hence, the distance covered in  

Q.7. Find the area of a rectangular park which is m long andm broad.
Ans. 

Area of the rectangular park = Length of the park × Breadth of the park     (∵ Area of rectangle = Length × Breadth)

Therefore, the area of the rectangular park is 610m².

Q.8. Find the area of a square plot of land whose each side measures metres.
Ans.
Area of the square plot = Side × Side = (Side)²  = a²  (Because the area of the square is a², where a is the side of the square)

Therefore, the area of the square plot is

Q.9. One litre of petrol costs What is the cost of 34 litres of petrol?
Ans.
Cost of 1 litre of petrol =
Cost of 34 litres of petrol =Rs.
So, the cost of 34 litres of petrol is

Q.10. An aeroplane covers 1020 km in an hour. How much distance will it cover in hours?
Ans.
Distance covered by the aeroplane in

= 4250 km
Therefore, the distance covered by the aeroplane is 4250 km.

Q.11. The cost ofmetres of cloth iswhat is the cost of one metre of cloth?
Ans.
Cost of m of cloth =
So, the cost of 1 m of cloth = Rs. 

Hence, the cost of 1 m of cloth is

Q.12. A cord of lengthm has been cut into 26 pieces of equal length. What is the length of each piece?
Ans.

Length of each piece of the cord =

Hence, the length of each piece of the cord is metres.

Q.13. The area of a room is If its breadth is  metres, what is its length?
Ans.
Area of a room = Length × Breadth
Thus, we have:


Hence, the length of the room is 12 metres.

Q.14.
The product of two fractions is If one of the fractions isfind the other.
Ans. Let the other fraction be x.
Now, we have:



Hence, the other fraction is

Q.15. In a school,of the students are boys. If there are 240 girls, find the number of boys in the school.
Ans.
If of the students are boys, then the ratio of girls is
Now, let x be the total number of students.
Thus, we have:


Hence, the total number of students is 640.
Now,
Number of boys = Total number of students - Number of girls
= 640 − 240

= 400
Hence, the number of boys is 400.

Q.16. After readingof a book, 40 pages are left. How many pages are there in the book?
Ans. Ratio of the read book =
Ratio of the unread book =

Let x be the total number of pages in the book.
Thus, we have:


Hence, the total number of pages in the book is 180.

Q.17.
Rita had Rs 300. She spent 1/3 of her money on notebooks and 1/4 of the remainder on stationery items. How much money is left with her?
Ans.
Amount of money spent on notebooks =

∴ Money left after spending on notebooks = 300 − 100
= 200
Amount of money spent on stationery items from the remainder =

∴ Amount of money left with Rita = 200−50
= Rs 150

Q.18. Amit earns Rs. 32000 per month. He spends 1/4 of his income of food; 3/10 of the remainder on house rent and of the remainder on the education of children. How much money is still left with him?
Ans.
Amit's income per month = Rs. 32,000
Money spent on food = of Rs.
Remaining amount = Rs. 32,000 − Rs. 8,000 = Rs.24,000
Money spent on house rent =
Money left = Rs. 24,000 − Rs.7,200 = Rs.16,800
Money spent on education of children =
Amount of money still left with him =  Rs.16,800 − Rs.4,000 = Rs.12,800

Q.19. If of a number exceeds itsby 44, find the number.
Ans.

Let x be the required number.

We know that of the number exceeds its by 44.
That is,






Hence, the number is 140.

Q.20. At a cricket test match of the spectators were in a covered place while 15000 were in open. Find the total number of spectators.
Ans. Ratio of spectators in the open
 

Total number of spectators in the open = x
Then,


Hence, the total number of spectators is 21,000