RS Aggarwal 2021-2022 for Class 6 Maths Solutions Chapter 10- Ratio, Proportion And Unitary Method
RS Aggarwal Class 6 Math Solution Chapter 10- Ratio, Proportion And Unitary Method, Test Paper-10 is available here. RS Aggarwal Class 6 Math Solutions are solved by expert teachers in step by step, which help the students to understand easily. RS Aggarwal textbooks are responsible for a strong foundation in Maths. These textbook solutions help students in exams as well as their daily homework routine. The solutions included are easy to understand, and each step in the solution is described to match the students’ understanding.
Rs Aggarwal Class 6 Math Solution Chapter 10- Ratio, Proportion And Unitary Method
Test Paper-10
A.1. Find the ratio of:
(a) 90 cm to 1.05 m
(b) 35 minutes to an hour
(c) 150 ml to 2 L
(d) 2 dozens to a score
Solution:
(a) 90 cm : 1.05 m
or, 90 cm : 105 cm
= `frac\{cancel 90^6}{cancel 105^7}`
= `frac\{6}{7}` = 6:7
(b) 35 minutes to an hour
or, 35 minutes : 60 minutes
= `frac\{cancel 35^7}{cancel 60^12}`
= `frac\{7}{12}` = 7 : 12
(c) 150 mL to 2 L
or, 150 L : 2000 L
= `frac\{cancel 150^3}{cancel 2000^40}`
= `frac\{3}{40}` = 3 : 40
(d) 2 dozens to a score
or, 24 : 20
= `frac\{cancel 24^6}{cancel 20^5}`
= `frac\{6}{5}` = 6 : 5
2. The ratio of zinc and copper in an alloy is 7 : 9. If the weight of copper in the alloy is 2.6 kg, find the weight of zinc in it.
Solution:
Ratio of zinc and copper in an alloy is = 7 : 9
Let the weight of zinc and copper be (7x) and (9x), respectively.
Now, the weight of a copper = 12.6 kg (given)
∴ 9x = 12.6
⇒ x = `frac\{12.6}{9}` = 1.4
∴ Weight of zinc = 7x = 7 × 1.4 = 9.8 kg
3. Divide Rs. 1400 among A, B and C in the ratio 2 : 3 : 5.
Solution:
Sum of ratio = 2 + 3 + 5 = 10
Total money = Rs 1400
Then, share of A = `frac\{2}{10}` × Rs 1400
= Rs `frac\{cancel 2800^280}{cancel 10}`
= Rs 280
Share of B = `frac\{3}{10}` × Rs 1400
= Rs `frac\{cancel 4200^420}{cancel 10}`
= Rs 420
Share of C = `frac\{5}{10}` × Rs 1400
= Rs `frac\{cancel 7000^700}{cancel 10}`
= Rs 700
4. Prove that (5 : 6) > (3 : 4).
Solution:
5 : 6 = `frac\{5}{6}` and 3 : 4 = `frac\{3}{4}`
By making their denominators same:
(Taking the L.C.M. of 6 and 4, which is 24.)
Consider, 5 : 6
`frac\{5 × 4}{6 × 4}` = `frac\{20}{24}`
And, `frac\{3 × 6}{4 × 6}` = `frac\{18}{24}`
As 20 > 18
Clearly, (5 : 6) > (3 : 4)
5. 40 men can finish a piece of work in 26 days. How many men will be needed to finish it in 16 days?
Solution:
Men needed to finish a piece of work in 26 days = 40
Men needed to finish it in 1 day = 26 × 40 = 1040
Men needed to finish it in 16 days = `frac\{cancel 1040^65}{cancel 16}` = 65
6. In an army camp, there were provisions for 425 men for 30 days. How long did the provisions last for 375 men?
Solution:
Provisions last for 425 men = 30 days
Provisions last for 1 men = 30 × 425 = 12750 days.
Provisions last for 375 men = `frac\{cancel 12750^34}{cancel 375}` = 34 days
Hence, provisions will last for 34 days for 375 men.
7. Find the value of x when 36 : x : : x : 16.
Solution:
Product of means = Product of extremes
`x × x` = 36 × 16
⇒ `x^2` = 576
⇒ `x^2` = `24^2`
⇒ x = 24
8. Show that 48, 60, 75 are in continued proportion.
Solution:
Product of means = 60 × 60 = 3600
Product of extremes = 48 × 75 = 3600
So product of means = Product of extremes
Hence, 48, 60, 75 are in continued proportion.
B. Mark (✔) against the correct answer in each of the following:
9. Two numbers are in the ratio 3 : 5 and their sum is 96. The larger number is
(a) 36
(b) 42
(c) 60
(d) 70
Solution: The correct option is (c) 60
Let the two number be 3x and 5x
A\q,
3x + 5x = 96
⇒ 8x = 96
⇒ x = `frac\{cancel 96^12}{cancel 8}` = 12
The numbers are:
3x = 3 × 12 = 36
5x = 5 × 12 = 60
The largest number = 60
10. A car travels 288 km in 4 hours and a train travels 540 km in 6 hours. The ratio of their speeds is
(a) 5 : 4
(b) 4 : 5
(c) 5 : 6
(d) 3 : 5
Solution: The correct option is (b) 4 : 5
Speed of the car = `frac\{distance}{time}` = `frac\{cancel 288^72}{cancel 4}` = 72 km/hr
Speed of the train = `frac\{distance}{time}` = `frac\{cancel 540^90}{cancel 6}` = 90 km/hr
Ratio of their speeds = 72 : 90 = `frac\{cancel 72^4}{cancel 90^5}` = 4 : 5
11. The first three terms of a proportion are 12, 21 and 8 respectively. The 4th term is
(a) 18
(b) 16
(c) 14
(d) 20
Solution: The correct option is (c) 14
Let the 4th term be x, such that we have:
12 : 21 : : 8 : x
Now, we know:
Product of extremes = Product of means
12x = 21 × 8
x = `frac\{cancel 168^14}{cancel 12}` = 14
12. The ratio 92 : 115 in simplest form is
(a) 23 : 25
(b) 18 : 23
(c) 3 : 5
(d) 4 : 5
Solution: The correct option is (d) 4 : 5
92 : 115
`frac\{92}{115}` = `frac\{92 ÷ 23}{115 ÷ 23}` = `frac\{4}{5}`
13. If 57 : x : : 51 : 85. then the value of x is
(a) 95
(b) 76
(c) 114
(d) none of these
Solution: The correct option is (a) 95
Given :
57 : x : : 51 : 85
We know:
Product of means = Product of extremes
51x = 57 × 85
x = `frac\{cancel 4845^95}{cancel 51}` = 95
14. If 4 : 5 : : x : 45, then the value of x is
(a) 54
(b) 60
(c) 36
(d) 30
Solution: The correct option is (c) 36
Given:
4 : 5 : : x : 45
We know:
Product of mean = Product of extremes
5x = 4 × 45
x = `frac\{cancel 180^36}{cancel 5}` = 36
15. If a, b, c are in proportion, then
(a) `a^2` = bc
(b) `b^2` = ac
(c) `c^2` = ab
(d) none of these
Solution: The correct option is (b) `b^2` = ac
Given:
a, b, c are in proportion, such that we have:
a : b : : b : c
Now, we know:
Product of means = Product of extremes
b × b = a × c
`b^2` = ac
16. 10 boys can dig a pitch in 12 hours. How long will 8 boys take to do it?
(a) 9 hrs 36 min
(b) 15 hrs
(c) 6 hrs 40 min
(d) 13 hrs 10 min
Solution: The correct option is (b) 15 hrs.
Time taken by 10 boys to dig a pitch = 12 hours
Time taken by 1 boy to dig a pitch = 12 × 10 = 120 hours
Time taken by 8 boys to dig a pitch = `frac\{cancel 120^15}{cancel 8}` = 15 hours
17. In covering 148 km, a car consumes 8 litres of petrol. How many kilometres will it go in 10 litres of petrol?
(a) 172 km
(b) 185 km
(c) 205 km
(d) 266.4 km
Solution: The correct option is (b) 185 km
Distance covered in 8 litres of petrol = 148 km
Distance covered in 1 litre of petrol = `frac\{148}{8}` km
Distance covered in 10 litres of petrol = 10 × `frac\{148}{8}`
= `frac\{cancel 1480^185}{cancel 8}`
= 185 km
C. 18. Fill in the blanks.
(i) `frac\{14}{ 21}` = `frac\{⬜}{3}` = `frac\{6}{⬜}`
(ii) 90 cm: 1.5 m = .......
(iii) If 36 : 81 : : x : 63, then x = ........
(iv) If 25, 35, x are in proportion, then x = …...
(v) If 9, x, x, 49 are in proportion, then x = ....... .
Solution:
(i) `frac\{14}{ 21}` = `frac\{⬜}{3}`
⬜ = `frac\{14 × 3}{21}` = `frac\{cancel 42^2}{cancel 21}` = 2
and, `frac\{2}{3}` = `frac\{6}{⬜}`
⬜ = `frac\{6 × 3}{2}` = `frac\{cancel 18^9}{cancel 2}` = 9
(ii) 90 cm : 1.5 m
or, 90 cm : 150 cm
= `frac\{90}{150}`
= `frac\{90 ÷ 30}{150 ÷ 30}`
= `frac\{3}{5}`
(iii) If 36 : 81 : : x : 63
Product of means = Product of extremes
81x = 36 × 63
x = `frac\{cancel 2268^28}{cancel 81}`
x = 28
(iv) Given:
25, 35, x are in proportion.
25 : 35 : : 35 : x
Now, we know:
Product of extremes = Product of means
25 × x = 35 × 35
25x = 1225
x = `frac\{cancel 1225^49}{cancel 25}` = 49
(v) Given:
9, x, x, 49 are in proportion.
9 : x : : x : 49
Now, we know:
Product of means = Product of extremes
` x × x` = 9 × 49
`x^2` = 441
`x^2` = `21^2`
x = 21
D.19. Write 'T' for true and 'F' for false for each of the statements given below:
(i) 30, 40, 45, 60 are in proportion.
(ii) 6 : 8 and 9 : 12 are equivalent ratios of 3 : 4.
(iii) a dozen : a score = 5 : 3.
(iv) 60 p : Rs. 3 = 1 : 5.
एक टिप्पणी भेजें
एक टिप्पणी भेजें