Advertisements
Advertisements
प्रश्न
Find two numbers such that the mean proportional between them is 12 and the third proportional to them is 96.
Advertisements
उत्तर
Let a and b be the two numbers, whose mean proportional is 12.
∴ ab = 122
`=>` ab = 144
`=> b = 144/a` ...(i)
Now, third proportional is 96
∴ a : b :: b : 96
`=>` b2 = 96a
`=> (144/a)^2 = 96a`
`=> (144)^2/a^2 = 96a`
`=> a^3 = (144 xx 144)/96`
`=>` a3 = 216
`=>` a = 6
`b = 144/6 = 24`
Therefore, the numbers are 6 and 24.
संबंधित प्रश्न
Find the value of the unknown in the following proportion :
3 : 4 : : p : 12
Find the fourth proportion to the following:
0.7, 4.9 and 1.6
If a : b = c : d; then show that (ax+ by) : b = (cx+ dy) : d
If a : b : : c : d, then prove that
2a+7b : 2a-7b = 2c+7d : 2c-7d
If a, 12, 16 and b are in continued proportion find a and b.
Determine if the following numbers are in proportion:
4, 6, 8, 12
If the cost of a dozen soaps is Rs 285.60, what will be the cost of 15 such soaps?
If `a/c = c/d = c/f` prove that : `(a^2)/(b^2) + (c^2)/(d^2) + (e^2)/(f^2) = "ac"/"bd" + "ce"/"df" + "ae"/"df"`
If a, b, c and d are in proportion, prove that: `(a + c)^3/(b + d)^3 = (a(a - c)^2)/(b(b - d)^2)`
If x, 2, 10 and y are in continued proportion, the values of x and y are respectively:
