Question

68. What number should be added to each of the number 103, 135, 110 and 144 so that the resulting numbers are in proportion?
103,135, 110 और 144 में प्रत्येक संख्या में कौन सी संख्या जोड़ी जानी चाहिए कि जिसके परिणामस्वरूप प्राप्त संख्याएं अनुपात में हों?
(a) 12
(b) 15
(c) 9
(d) 6​

Answer 1

Answer:

15is the correct answer

Answer 2

$Let \: the \: number\: \pink {x} \: should \:be \\:added \\to \: to \:each \: of \:the \: number \: 103, 135 , 110 \\and\: 144 \: so \: that \: the \: resulting \: numbers \\are \: in \: proportion$

$Now, (103+x), (135+x), (110+x) \:and \:(144+x) \\are \: in \: proportion$

$\implies (103+x) :(135+x)=(110+x) :(144+x)$

$\pink { Product \:of \: the \:extremes }\\= \blue { Product \:of \: the \:means }$

$\implies (103+x)(144+x) = (135+x)(110+x)$

$\implies 103(144+x)+x(144+x)\\=135(110+x)+x(110+x)$

$\implies 14832 + 103x+144x+x^{2} \\= 14850 + 135x+110x+x^{2}$

$\implies 14832 + 247x + x^{2} = 14850+245x+x^{2}$

$\implies 14832 + 247x = 14850+245x$

$\implies 247x - 245x = 14850 - 14832$

$\implies 2x = 18$

$\implies x = \frac{18}{2}$

$\implies x = 9$

Therefore.,

$\red{ Number \: should \:be \:added\:is } \green { = 9 }$

$Option \: \pink { ( c ) } \: is \: correct$

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