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Maths Ace Class 8 Solutions Chapter 10 Direct and Inverse Variations
Welcome to NCTB Solutions. Here with this post we are going to help 8th class students for the Solutions of Maths Ace Prime Class 8 Math Book, Chapter 10, Direct and Inverse Variations. Here students can easily find step by step solutions of all the problems for Direct and Inverse Variations, Exercise 10.1, 10.2 and 10.3 Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 10 solutions.
Direct and Inverse Variations Exercise 10.1 Solution :
Question no – (1)
Solution :
From given table,
x2/60 = 3/45
= 45 × x2 = 3 × 60
= x2 = 3 × 60/45
= 4
And, 9/y3 = 3/45
= 3y3 = 9 × 45
= y3 = 9 × 45/3
= 135
Therefore, the value of x2 will be 4 and y3 will be 135.
Question no – (2)
Solution :
As per the given question,
Raj bought 35 packs of crayons for = Rs 700.
Roy bought = 7 packs of the same crayons
∴ Cost of 7 pack crayons,
First, 1 pack cost,
= 700/35
= 20 Rs
Now, Roy pay,
= (20 × 7)
= 140 Rs
Therefore, the Ray will pay 140 Rs.
Question no – (3)
Solution :
In the given question,
Cost of 4 kg of rice is = Rs 90,
Rice can be purchased with = Rs 247.50
Let, x kg purchased,
∴ 4 : 90 :: x : 247..50
= 4/90 = x/247.50
= x = 247.50 × 4/90
= 11 kg
Therefore, 11 kg rice can be purchased with Rs 247.50.
Question no – (4)
Solution :
According to the question,
x varies directly with 5y and x = 15 when y = 75 ,
∴ The value of y,
= y = 5x
= 5 × 7
= 35
Therefore, the value of y will be 35.
Question no – (5)
Solution :
x = 3y + 5
= 3 × 5/3 + 5
= 5 + 5
= 10
When, y = 5/3, x = 10
Now, 3y + 5 = 36
= 3y = 36 – 5
= 31
= y = 31/3
Therefore, the value of y will be 31/3.
Direct and Inverse Variations Exercise 10.2 Solution :
Question no – (1)
Solution :
a and b very inversely,
∴ 32 × b2 = 64
= b2 = 64/32
= b2 = 2
And, a3 × 0.5 = 64
= a3 = 64 × 10/5
= 128
Thus, the value of a3 will be 128 and value of b2 will be 2.
Question no – (2)
Solution :
Given in the question,
= x × 1/y
= xy = k
When x = 9, y = 21
xy = 9 × 21 = 189
When y = 7
∴ x × 7 = 189
= x = 189/7
= x = 27
Therefore, the value of x will be 27.
Question no – (3)
Solution :
(a)
| A | 4 | 8 | 12 |
| B | 32 | 16 | 32/3 |
= This is inverse variation.
(b)
| A | 1 | 3 | 27 |
| B | 3 | 9 | 81 |
= This is direct variation.
Question no – (4)
Solution :
Let, x books can buy
∴ Total money,
= (15 × 30)
= 450 Rs
Total cost increase 45 Rs
∴ Per books cost increase
= 45/15 = 3 Rs
New cost per book
= Rs (30 + 3)
= 3 Rs
Total book she bought,
= 450/33
= 13.6
∴ 13 books can buy
∴ Money left,
= 450 – (33 × 13)
= 450 – 429
= 21 Rs
Therefore, Rita can buy 13 books, and also Rs. 21 will be left with her.
Question no – (5)
Solution :
As per the given question,
Enough food for 8 students for 30 days.
12 more students join
∴ Food will last,
= 8 × 30 = 20 × x
= x = 8 × 30/20
= 12
Therefore, the food will last 12 days.
Question no – (6)
Solution :
1st, Distance
= (60 × 6) km
= 360 km
2nd, Distance
= 360 km
Speed = 45 km/h
∴ Time = 360/45
= 8 hr
Therefore, it will take 8 hours to cover the same distance.
Question no – (7)
Solution :
Rs 3200 for 20 students for 30 days so per student per day expenditure is,
= 3200/ (20 × 30)
= 5.33 Rs
∴ 1 day expense for 30 students,
= (5.33 × 30)
= 160 Rs
∴ For Rs 2400, No of day to use,
= 2400/160
= 15 days
Therefore, the food will last 15 days.
Question no – (8)
Solution :
Labour required for book,
= 6 × 10/5
= 12 men’s
For 4 books, it take
= (12 × 4) men’s labour
= 48 men’s labour
No of days required,
= 48/6
= 6 days
Therefore, it will take 6 days to the copy the book.
Question no – (9)
Solution :
Given in the question,
Two workers earn = Rs 2400 each for two hours work.
If there are = 5 workers
Let, 5 workers earn = ‘x’
∴ 2x = 5 × 2400
= x = 5 × 2400/2
= 6000 Rs
Therefore, they will earn 6000 Rs.
Direct and Inverse Variations Exercise 10.3 Solution :
Question no – (1)
Solution :
We know, Time = 425/50
= 8.5 hr
∴ He will reach at,
= (10 h 30 + 8 h 30)
= 7 pm
Therefore, he will reach the place at 7 pm.
Question no – (2)
Solution :
According to the question,
A water tank had three inlets, fill the tank in 20, 40 and 30 minutes,
Part filled by (A + B + C) in 1 min,
= (1/20 + 1/30 + 1/40)
= 6 + 4 + 3/120
= 13/120
∴ Time take,
= 120/13
= 9.23 min
Therefore, all three inlets work together to fill the tank in 9.23 min.
Question no – (3)
Solution :
They work together,
= (1/20 + 1/25)
= 5 + 4/100
= 9/100
∴ Time taken,
= 100/9
= 11 1/11 hours
Therefore, it will take 11 1/11 hours.
Question no – (4)
Solution :
According to the question,
Raj and Saleem can type 20 and 40 words, in a minute.
Saleem complete a task in = 5 minutes.
Now, Raj 8 Saleem can type 20 and 40 words
Raj need twice the time take by Saleem
= 40/20 = 2
∴ 2 × 5 = 10 min
Therefore, Time taken by Raj will be 10 min.
Question no – (5)
Solution :
L.C.M of 30, 45, 30 = 180
∴ A fill 1 hour = 180/30 = 6 L
∴ B fill in 1 hour = 180/45 = 4 L
∴ C empties in 1 hour
= 180/30
= 6L
∴ A + B – C
= 6 + 4 – 6
= 4 L
∴ Time taken,
= 180/4
= 45 min
Therefore, it will take 45 min to fill the tank.
Question no – (6)
Solution :
P’s 1 day work = 1/3
(p + Q) 1 day work = 1/2
∴ Q alone 1 day work,
= (1/2 – 1/3)
= 3 – 2/6
= 1/6
Therefore, Q alone will take 6 days.
Next Chapter Solution :
👉 Chapter 11 👈
