Advertisements
Advertisements
प्रश्न
If a, b, c and d are in proportion, prove that: (ma + nb) : b = (mc + nd) : d
उत्तर
∵ a, b, c, d are in proportion
`a/b = c/d` = k(say)
a = bk, c = dk.
(ma + nb) : b = (mc + nd) : d
⇒ `"ma + nb"/b = "mc + nd"/d`
L.H.S. = `"mbk + nb"/b`
= `(b("mk + n"))/b`
= mk + n
R.H.S. = `"mc + nd"/d`
= `"mdk + nd"/d`
= `(d("mk + n"))/d`
= mk + n.
∴ L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
If `(4m + 3n)/(4m - 3n) = 7/4`, use properties of proportion to find `(2m^2 - 11n^2)/(2m^2 + 11n^2)`
Find the fourth proportion to the following:
3,5 and 15
Find the smallest number that must be subtracted from each of the numbers 20, 29, 84 and 129 so that they are in proportion.
Find the third proportional to:
x - y, x2 - y2
If a, b, c, d are in continued proportion, prove that:
(a2 + b2 + c2) (b2 + c2 + d2) = (ab + bc + cd)2.
Find the mean proportion of: `(1)/(12) and (1)/(75)`
The weight of 65 books is 13 kg.
(i) What is the weight of 80 such books?
(ii) How many such books weigh 6.4 kg?
Write the mean and extreme terms in the following ratios and check whether they are in proportion.
78 litre is to 130 litre and 12 bottles is to 20 bottles
Write the mean and extreme terms in the following ratios and check whether they are in proportion.
400 gm is to 50 gm and 25 rupees is to 625 rupees
Determine if the following are in proportion.
33, 121, 9, 96
