if x:3 is proportion with 15:5 find the value of x
Answers
Step-by-step explanation:
Determine if the following are in proportion. If yes write them in proper form.
(i) 32, 48, 140, 210; (ii) 6, 9, 10 and 16
Solution:
(i) 32, 48, 140, 210
32 : 48 = 32/48 = 2/3 = 2 : 3
140 : 210 = 140/210 = 2/3 = 2 : 3
So, 32 : 48 = 140 : 210
Therefore, 32, 48, 140, 210 are in proportion.
i.e., 32 : 48 :: 140 : 210
(ii) 6, 9, 10 and 16
6 : 9 = 6/9 = 2/3 = 2 : 3
10 : 16 = 10/16 = 5/8 = 5 : 8
Since, 6 : 9 ≠ 10 : 16 therefore, 6, 9, 10 and 16 are not in proportion.
2. The numbers 8, x, 9 and 36 are in proportion. Find x.
Solution:
The numbers 8, x, 9 and 36 are in proportion
⇒ 8 : x = 9 : 36
⇒ x × 9 = 8 × 36, [Since, the product of the means = the product of the extremes]
⇒ x = (8 × 36)/9
⇒ x = 32
3. If x : 15 = 8 : 12; find the value of x.
Solution:
⇒ x × 12 = 15 × 8, [Since, the product of the extremes = the product of the means]
⇒ x = (15 × 8)/12
⇒ x = 10
4. If 4, x, 32 and 40 are in proportion, find the value of x.
Solution:
4, x, 32 and 40 are in proportion, i.e., 4 : x :: 32 : 40
Now, product of extremes = 4 × 40 = 160
And product of means = x × 32
We know that in a proportion product of extremes = product of means
i.e., 160 = x × 32
If we multiply 32 by 5, we get 160
i.e., 5 × 32 = 160
So, x = 5
Hence, 4, 5, 32 and 40 are in proportion.
Answer:
If x : 3 :: 15 : 5; find the value of x.
Solution:
⇒ x × 5 = 3 × 15, [Since, the product of the extremes = the product of the means]
⇒ x = (15 × 3)/5
⇒ x = 5