Advertisements
Advertisements
प्रश्न
If a, b, c and d are in proportion, prove that: (ma + nb) : b = (mc + nd) : d
Advertisements
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
Find the fourth proportion to the following:
(p2q - qr2 ), (pqr - pr2 ) and (pq2 - pr2)
Verify the following:
91 : 104 : : 119 : 136
If the cost of a dozen soaps is Rs 285.60, what will be the cost of 15 such soaps?
The cost of 4 dozen bananas is Rs 104. How many bananas can be purchased for Rs 6.50?
If 40 men can finish a piece of work in 26 days, how many men will be required to finish it in 20 days?
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 are in continued proportion, prove that: (a + b + c) (a – b + c) = a2 + b2 + c2
If a, b, c, d are in continued proportion, prove that: a : d = triplicate ratio of (a – b) : (b – c)
What is the term "d" called in the expression a : b :: c : d?
A picture frame’s length and width are in the ratio 4 : 3. If the length is 28 cm, what is the width?
