Question

sold 300 prices to duttagupta kolkata on the following terms
(a) list price ruppees 70 per pen
(b) trade discount 5% and cash discount 5% if payment is made with in 7 days of sale duttagupta made payment after 21 days Please say anybody it is urgent​

Answer 1

Explanation:

Answer:

The required increasing G.P will be 12 , 18 & 27 respectively .

Step-by-step explanation:

According to the Question

It is given that,

Product of three increasing numbers in GP is 5832

If we add 6 to the second number and 9 to the third number, then resulting numbers form an AP.

Let the first three terms of the given G.P be \sf \frac{a}{r} , a \; and \; arra,aandar respectively .

Product of given G.P = 5832

↠ a/r × a × ar = 5832

↠ a × a × a = 5832

↠ a³ = 5832

↠ a³ = 18 × 18 × 18

↠ a³ = 18³

↠ a = 18 .

And, also it is given that a/r , (a+6) & (ar+9) are in A.P (Given)

\begin{gathered}\dashrightarrow\sf\; 2\; (a+6) = \frac{a}{r} + ar + 9 \\\\\\\dashrightarrow\sf\; 2\; (18+6) = \frac{18}{r} + 18r + 9 \\\\\\\dashrightarrow\sf\; 2\; (24) = \frac{18}{r} + 18r + 9 \\\\\\\dashrightarrow\sf\; 48 -9 = \frac{18}{r} + 18r \\\\\\\dashrightarrow\sf\; 39 = \frac{18 + 18r^{2}}{r} \\\\\\\dashrightarrow\sf\; 39r = 18 + 18r^{2} \\\\\\\dashrightarrow\sf\; 18r^{2} -39r + 18 = 0\\\\\\\dashrightarrow\sf\; 6r^2 -13r + 6 = 0\\\\\\\dashrightarrow\sf\; 6r^2 - 9r - 4r + 6 = 0\\\end{gathered}⇢2(a+6)=ra+ar+9⇢2(18+6)=r18+18r+9⇢2(24)=r18+18r+9⇢48−9=r18+18r⇢39=r18+18r2⇢39r=18+18r2⇢18r2−39r+18=0⇢6r2−13r+6=0⇢6r2−9r−4r+6=0

\begin{gathered}\dashrightarrow\sf\; 3r(2r-3) -2(2r-3) = 0\\\\\\\dashrightarrow\sf\; (2r-3) (3r-2) = 0\\\\\\\dashrightarrow\sf\; r = \frac{3}{2} \; r = \frac{2}{3}\end{gathered}⇢3r(2r−3)−2(2r−3)=0⇢(2r−3)(3r−2)=0⇢r=23r=32

As it is given that the G.P are in increasing order .

So we will take here r = 3/2

So, the required increasing G.P will be

\begin{gathered}\dashrightarrow\sf\; \frac{a}{r} = \frac{18}{\frac{3}{2} } = 18 \times\frac{2}{3} = 6\times\;2 = 12\\\\\\\dashrightarrow\sf\; a = 18 \\\\\\\dashrightarrow\sf\; ar = 18\times\; \frac{3}{2} = 9\times\; 3 =27 \\\\\\\boxed{\bf{{Hence,\; the\; required\; increasing \; GP \; are\; 12, 18 \; and \; 27}}}\end{gathered}⇢ra=2318=18×32=6×2=12⇢a=18⇢ar=18×23=9×3=27Hence,therequiredincreasingGPare12,18and27