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Sia ? 6 years, 6 months ago
LCM of rational number ={tex}\frac{{{\text{LCM of numerators}}}}{{{\text{HCF of denominators}}}}{/tex}
Numbers are {tex}\frac { 25 } { 10 } , \frac { 5 } { 10 } , \frac { 175 } { 1000 }{/tex}
Now, 25 = 5{tex}\times{/tex}5; 5 = 5{tex}\times{/tex}1; 175 = 5{tex}\times{/tex}5{tex}\times{/tex}7
LCM of (25, 5, 175) = 5{tex}\times{/tex}5{tex}\times{/tex}7 = 175
Also,
10 = 2{tex}\times{/tex}5; 1000 = 2{tex}\times{/tex}2{tex}\times{/tex}2{tex}\times{/tex}5{tex}\times{/tex}5{tex}\times{/tex}5
HCF of (10,10,1000) = 10
LCM of (2.5, 0.5, 0.175) ={tex}\frac { 175 } { 10 } = 17.5{/tex}
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Sia ? 6 years, 6 months ago
Let the cost price of an article be Rs. x. It is given that percentage gain is equal to cost price of the article.
Hence, percentage gain = x%
{tex}{/tex} {tex}{/tex}{tex}S\cdot P=C\cdot P(1+\frac{percentagegain)}{100}{/tex}[S.P is selling price]
{tex}\therefore{/tex}S.P. = {tex}x(1+\frac x{100}){/tex} = x + {tex}\frac { x ^ { 2 } } { 100 }{/tex}
Given, S.P. = Rs. 75
{tex}\Rightarrow x + \frac { x ^ { 2 } } { 100 } = 75{/tex}
{tex}\Rightarrow{/tex} 100x + x2 = 7500
{tex}\Rightarrow{/tex} x2 + 100x - 7500 = 0
{tex}\Rightarrow{/tex} x2 + 150x - 50x - 7500 = 0
{tex}\Rightarrow{/tex} x(x + 150) - 50(x +150) = 0
{tex}\Rightarrow{/tex} (x + 150) (x - 50) = 0
{tex}\Rightarrow{/tex} x + 150 = 0 or x - 50 = 0
Since the price cannot be negative, x {tex}\neq{/tex} -150.
{tex}\Rightarrow{/tex} x = 50
Thus, the cost price of an article =Rs. x = Rs. 50.
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Rashim Maan 7 years, 7 months ago
2Thank You