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.
APPEARS IN
संबंधित प्रश्न
If a, b, c are in continued proportion, show that: `(a^2 + b^2)/(b(a + c)) = (b(a + c))/(b^2 + c^2)`.
Check whether the following numbers are in continued proportion.
9, 12, 16
Find the value of the unknown in the following proportion :
3 : 4 : : p : 12
Find two nurnbers whose mean proportional is 12 and the third proportional is 324.
If a, b, c and dare in continued proportion, then prove that
(a+ d)(b+ c)-(a+ c)(b+ d)= (b-c)2
Find the third proportional to Rs. 3, Rs. 12
Find the value of x in each of the following proportions:
51 : 85 : : 57 : x
4.5 g of an alloy of copper and zinc contains 3.5 g of copper. What weight of copper will there be in 18.9 g of the alloy?
If 40 men can finish a piece of work in 26 days, how many men will be required to finish it in 20 days?
10 g of caustic soda dissolved in 100 mL of water makes a solution of caustic soda. Amount of caustic soda needed for 1 litre of water to make the same type of solution is ______.
