The Rice is mixed up!!

Algebra Level 2

The ratio in which rice at Rs. 7.2 7.2 a kg be mixed with rice at Rs. 5.7 5.7 a kg to produce a mixture worth Rs. 6.3 6.3 a kg be expressed as a : b a:b . Find ( a + b ) 2 (a+b)^{ 2 } .


The answer is 25.

Shreya R by Shreya R , 21, India

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2 solutions

Unstable Chickoy
Jun 15, 2014

7.2 x + 5.7 ( 1 − x ) = 6.3 7.2x + 5.7(1-x) = 6.3

x = 0.4 x = 0.4

a b = 0.4 1 − 0.4 = 2 3 \frac{a}{b} = \frac{0.4}{1-0.4} = \frac{2}{3}

( a + b ) 2 = ( 2 + 3 ) = 25 (a + b)^2 = (2 + 3) = \boxed{25}

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Anas Ahmed
Jun 2, 2014

Consider a sample mix of 1 kg Let amount of rice worth 7.2/kg be x% Let amount of rice worth 5.7/kg be y=(1-x)% Now 7.2x+5.7(1-x)=6.3 Hence, x=0.4 That is: a=40% rice at 7.2/kg and the rest b=60% at 5.7/kg Therefore: a/b=40%/60%=2/3 So, a+b=5 And (a+b)^2=5^2=25

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