RS Aggarwal Class 7 Math Eighth Chapter Ratio and Proportion Exercise 8B Solution
EXERCISE 8B
(1) Show that 30, 40, 45, 60 are in proportion.
Solution: We have,
Product of extremes = (30 × 60) = 1800
Product of means = (40 × 45) = 1800.
∴ Product of extremes = Product of means.
Hence, 30, 40, 45, 60 are in proportion.
(2) Show that 36, 49, 6, 7 are not in proportion.
Solution: We have,
Product of extremes = (36 × 7) = 252
Product of means = (49 × 6) = 294.
∴ Product of extremes ≠ Product of means.
Hence, 36, 49, 6, 7 are not in proportion.
(3) If 2 : 9 : : x : 27, find the value of x.
![](https://www.netexplanations.com/wp-content/uploads/2018/10/125571258.png)
(4) If 8 : x : : 16 : 35, find the value of x.
![](https://www.netexplanations.com/wp-content/uploads/2018/10/125571258-1.png)
(5) If x : 35 : : 48 : 60, find the value of x.
![](https://www.netexplanations.com/wp-content/uploads/2018/10/125571258-2.png)
(6) Find the fourth proportional to the numbers:
(i) 8, 36, 6
Solution: Let the fourth term be, x. Then,
![](https://www.netexplanations.com/wp-content/uploads/2018/10/125571258-3.png)
Hence, the fourth term is 27.
(ii) 5, 7, 30
Solution: Let the fourth term be, x. Then,
![](https://www.netexplanations.com/wp-content/uploads/2018/10/125571258-4.png)
Hence, the fourth term is 42.
(iii) 2.8, 14, 3.5
Solution: Let the fourth term be, x. Then,
![](https://www.netexplanations.com/wp-content/uploads/2018/10/125571258-5.png)
Hence, the fourth term is 17.5.
(7) If 36, 54, x are in continued proportion, find the value of x.
Solution: We have,
![](https://www.netexplanations.com/wp-content/uploads/2018/10/125571258-6.png)
Hence, x = 81.
(8) If 27, 36, x are in continued proportion, find the value of x.
Solution: We have,
![](https://www.netexplanations.com/wp-content/uploads/2018/10/125571258-7.png)
Hence, x = 48.
(9) Find the third proportional to:
(i) 8 and 12
Solution: Let the third proportional be x.
Then, the fourth proportional to 8, 12, 12 is x.
![](https://www.netexplanations.com/wp-content/uploads/2018/10/125571258-8.png)
Hence, the third proportional to 9 and 12 is 18.
(ii) 12 and 18
Solution: Let, the third proportional be x.
Then, the fourth proportional to 12 and 18, 18 is x.
![](https://www.netexplanations.com/wp-content/uploads/2018/10/125571258-9.png)
Hence, the third proportional is 27.
(iii) 4.5 and 6
Solution: Let the third proportional be x.
Then, the fourth proportional to 4.5 and 6, 6 is x.
![](https://www.netexplanations.com/wp-content/uploads/2018/10/125571258-10.png)
Hence, the third proportional is 8.
(10) If the third proportional to 7 and x is 28. Find the value of x.
Solution: We have,
![](https://www.netexplanations.com/wp-content/uploads/2018/10/125571258-11.png)
(11) Find the mean proportional between:
(i) 6 and 24
Solution: Let the mean proportional between 6 and 24 be x.
Then, 6 : x : : x : 24
or, x × x = 6 × 24
or, x2 = 144 = (12)2
or, x = 12
(ii) 3 and 27
Solution: Let the mean proportional between 3 and 27 be x.
Then, 3 : x : : x : 27
or, x × x = 3 × 27
or, x2 = 81 = (9)2
or, x = 9
(iii) 0.4 and 0.9
Solution: Let the mean proportional between 0.4 and 0.9 be x.
Then, 0.4 : x : : x : 0.9
or, x × x = 0.4 × 0.9
or, x2 = 0.36 = (0.6)2
or, x = 0.6
(12) What number must be added to each of the numbers 5, 9, 7, 12 to get the numbers which are in proportion?
Solution: Let the number to be added be x. Then,
![](https://www.netexplanations.com/wp-content/uploads/2018/10/125571258-12.png)
Hence, the required number is 3.
(13) What number must be subtracted from each of the numbers 10, 12, 19, 24 to get the numbers which are in proportion?
Solution: Let the number to be subtracted be x. then,
![](https://www.netexplanations.com/wp-content/uploads/2018/10/125571258-13.png)
Hence, the required number is 4.
(14) The scale of map is 1 : 5000000. What is the actual distance between two towns, if they are 4 cm apart on the map?
Solution: 1 cm on the map shows the distance = 5000000 cm.
![](https://www.netexplanations.com/wp-content/uploads/2018/10/125571258-14.png)
4 cm on the map shows the distance = (50 × 4) km = 200 km.
∴ Actual distance between the two towns is 200 km.
(15) At a certain time a tree 6 m high casts a shadow of length 8 metres. At the same time a pole casts a shadow of length 20 metres. Find the height of the pole.
Solution: Let the height of pole is x m.
![](https://www.netexplanations.com/wp-content/uploads/2018/10/125571258-15.png)
Hence, the height of the pole is 15 m.
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