This is an important ques from the Book ML Aggarwal class 10th,, chapter – 7, ratio and proportion.
In this question we have been given the two numbers and we have to find the third proportional to them.
Question 3, 7.2
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Find the third proportional to (i) 5, 10 (ii) 0.24, 0.6 (iii) Rs. 3, Rs. 12 (iv) 5 ¼ and 7.
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Solution:
(i) Consider x as the third proportional to 5, 10
5: 10 :: 10: x
It can be written as
5 × x = 10 × 10
x = (10 × 10)/ 5 = 20
Hence, the third proportional to 5, 10 is 20.
(ii) Consider x as the third proportional to 0.24, 0.6
0.24: 0.6 :: 0.6: x
It can be written as
0.24 × x = 0.6 × 0.6
x = (0.6 × 0.6)/ 0.24 = 1.5
Hence, the third proportional to 0.24, 0.6 is 1.5.
(iii) Consider x as the third proportional to Rs. 3 and Rs. 12
3: 12 :: 12: x
It can be written as
3 × x = 12 × 12
x = (12 × 12)/ 3 = 48
Hence, the third proportional to Rs. 3 and Rs. 12 is Rs. 48
(iv) Consider x as the third proportional to 5 ¼ and 7
5 ¼: 7 :: 7: x
It can be written as
21/4 × x = 7 × 7
x = (7 × 7 × 4)/ 21 = 28/3 = 9 1/3
Hence, the third proportional to 5 ¼ and 7 is 9 1/3.