Explanation
Multiplying equation $$(1) $$ with $$ 4 $$ we get, $$ 28x + 24y = 284 $$ ----- equation $$(3) $$
Multiplying equation $$(2) $$ with $$ 3 $$ we get, $$ 15x - 24y = - 69 $$ ----- equation $$ (4)$$
Adding equations $$ (4) $$ and $$ (3) $$, we get $$ 43x = 215 => x = 5 $$
Substituting $$x = 5 $$ in the equation $$ (2) $$, we get
$$ 5(5) - 8y = -23 => y = 6 $$
Substituting $$ y = \dfrac {1}{4} $$ in the equation $$ (1) $$, we get
$$ x + \dfrac {1}{4} = 2(x)( \dfrac {1}{4}) $$
$$\therefore x = -\dfrac {1}{2} $$
Multiplying eq(1) with $$3 $$ we get,
$$ \dfrac {60}{x+y} + \dfrac {9}{x-y} = 21 $$ ...(3)
Multiplying eq(2) with $$ 4 $$ we get,
$$\dfrac {32}{x-y} - \dfrac {60}{x+y} = 20 $$ ...(4)
Adding eq(3) and eq(4), we get
$$\dfrac {41}{x-y} = 41 => x - y = 41 $$ ...(5)
Substituting $$ x-y = 41 $$ in the eq(1), we get
$$ \dfrac {20}{x+y} + \dfrac {3}{1} = 7 => \dfrac {20}{x+y} = 4 => x +y = 5 $$ ... (6)
Adding eq(5) and eq(6), we get
$$ 2x = 6 => x = 3 $$
Substituting $$ x = 3 $$ in the eq(5), we get
$$ 3-y = 1 => y = 2 $$
As per the statement, "If A gives 10 pencils to B, then B will have twice as many as A":
$$ \implies 2(x - 10) = y + 10$$
$$ 2x - y = 30 $$ --- (1)Also, as per the statement, "if B gives 10 pencils to A, then they will have the same number of pencils"
$$\implies x + 10 = y - 10 $$
$$x - y = -20 $$ --- (2)
Subtracting equation $$ (2) $$ from $$ (1) $$, we get:
$$2x-y-x+y=30+20$$
$$ x = 50$$
Substituting $$ x = 50 $$ in equation $$ (2) $$, we get:
$$ 50 -y = -20$$
$$\implies y = 70 $$
So, A has $$50$$ pencils and B has $$70$$ pencils.
Multiplying equation $$ (1) $$ with $$ 5 $$We get $$ 5x + 5y = 35 $$ $$...(3)$$Adding equations $$ (2) $$ and $$ (3), $$ $$4x-5y=-8$$ $$5x+5y=35$$ ______________ $$9x\ \ \ \ \ \ \ \ =27$$
$$ \Rightarrow 9x = 27 $$$$\Rightarrow x = 3 $$Substituting $$ x = 3 $$ in the equation $$ (1) $$ We get $$ 3 + y = 7 $$$$\Rightarrow y = 4 $$
Hence, the fraction is $$\dfrac34$$
Multiplying equation $$(1) $$ with $$ 3 $$ we get, $$ 3x + 3y = 552 $$ ----- equation $$(3) $$
Adding equations $$2 $$ and $$ 3 $$, we get $$ 10x = 636 => x = 63.6 $$
Substituting$$ x = 63.6 $$ in the equation $$ (2) $$, we get $$ 63.6 + y = 184 =>y = 120.4$$
Thus , the parts are $$ 63.6 ; 120.4 $$
Multiplying equation $$ (2) $$ with $$ 1.05 $$ we get, $$ 1.1235x + 1.1025y = 1223.25 $$ ----- equation $$ (4) $$
Subtracting equation $$(4) $$ from $$ (3) $$, we get $$ 0.0424y = 25.44 \Rightarrow y = 600 $$
Substituting $$ y = 600 $$ in the equation $$ (2) $$, we get $$ 1.07x + 1.05(600) = 1165 \Rightarrow x = 500 $$Hence, cost price of $$A$$ is Rs. $$ 500 $$ and of $$B$$ is Rs. $$ 600 $$
Substituting $$ y = 18 $$ in the equation $$ (1) $$, we get $$ x + 18 = 40 => x = 22 $$
Hence $$ 22 kg $$ and $$ 18 kg $$ of two types of sweets were bought.
Substituting $$ x = 600 $$ in the equation $$ (1) $$, we get $$ 600 + y = 1250 \Rightarrow y = 650 $$
Please disable the adBlock and continue. Thank you.
