(a) If first, second and third terms of a
proportion are 2, 3 and 90, respectively,
then find the fourth term of the
proportion.
(b) If first, second and fourth terms of a
proportion are 10, 7 and 35, respectively,
then find its third term.
(c) If second, third and fourth terms of a
proportion are 18, 10 and 20, respectively,
then find its first term.
(d) If first, third and fourth terms of
a proportion are 1.5, 4.5 and 9.0,
respectively, then find its second term.
and explain each one
Answers
Answer:
1. Check whether the two ratios form a proportion or not:
(i) 6 : 8 and 12 : 16; (ii) 24 : 28 and 36 : 48
Solution:
(i) 6 : 8 and 12 : 16
6 : 8 = 6/8 = 3/4
12 : 16 = 12/16 = 3/4
Thus, the ratios 6 : 8 and 12 : 16 are equal.
Therefore, they form a proportion.
(ii) 24 : 28 and 36 : 48
24 : 28 = 24/28 = 6/7
36 : 48 = 36/48 = 3/4
Thus, the ratios 24 : 28 and 36 : 48 are unequal.
Therefore, they do not form a proportion.
2. Fill in the box in the following so that the four numbers are in proportion.
5, 6, 20, ____
Solution:
5 : 6 = 5/6
20 : ____ = 20/____
Since the ratios form a proportion.
Therefore, 5/6 = 20/____
To get 20 in the numerator, we have to multiply 5 by 4. So, we also multiply the denominator of 5/6, i.e. 6 by 4
Thus, 5/6 = 20/6 × 4 = 20/24
Hence, the required numbers is 24
3. The first, third and fourth terms of a proportion are 12, 8 and 14 respectively. Find the second term.
Solution:
Let the second term be x.
Therefore, 12, x, 8 and 14 are in proportion i.e., 12 : x = 8 : 14
⇒ x × 8 = 12 × 14, [Since, the product of the means = the product of the extremes]
⇒ x = (12 × 14)/8
⇒ x = 21
Therefore, the second term to the proportion is 21.
Answer:
x = 9 will be the answer
hope it helps