The cost of 6 pen and 4 pencils is Rs 60 and the cost of of 4 pen and 6 pencil is Rs 40 then find the cost of one pen and one pencil.
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The cost of 6 pen and 4 pencils is Rs 60 and the cost of of 4 pen and 6 pencil is Rs 40 then find the cost of one pen and one pencil.
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Step-by-step explanation:
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\begin{gathered}so \: here \: \\ secA + tanA =x \\ ie \: tan \: A = x - sec \: A\end{gathered}
sohere
secA+tanA=x
ietanA=x−secA
\begin{gathered}so \: now \: using \\ 1 + tan ^{2} A = sec {}^{2} A \\ 1 + (x - sec \: A) {}^{2} = sec {}^{2} A \\ 1 + x {}^{2} + sec {}^{2} A - 2sec \: A.x = sec {}^{2} A \\ 1 + x {}^{2} - 2sec \: A.x = 0 \\ ie \: 1 + x {}^{2} = 2secA.x \\ sec \: A = 1 + x {}^{2} /2x \\ \\ \end{gathered}
sonowusing
1+tan
2
A=sec
2
A
1+(x−secA)
2
=sec
2
A
1+x
2
+sec
2
A−2secA.x=sec
2
A
1+x
2
−2secA.x=0
ie1+x
2
=2secA.x
secA=1+x
2
/2x
\begin{gathered}thus \: value \: of \: sec \: A \: (in \: terms \: of \: x) \: is \: 1 + x {}^{2} /2x \\ \end{gathered}
Answer:
Let a pen cost S and a pencil L.
6S + 3L = 60, or
2S + L = 20 …(1)
5S + 2L = 48 …(2)
Multiply (1) by 2 to get
4S + 2L = 40 …(3)
Subtract (3) from (2)
S = 8. So each pen is 8.
From (1), L = 20 - 2S = 20–16 = 4.
Each pencil is 4 and each pen is 8.