ISRO2020-55

Question

If $x+2y=30$, then $\left(\dfrac{2y}{5}+\dfrac{x}{3} \right) + \left (\dfrac{x}{5}+\dfrac{2y}{3} \right)$ will be equal to

• A. $8$
• B. $16$
• C. $18$
• D. $20$

Comments

$\frac{1}{5}(x+2y)+ \frac{1}{3}(x+2y)$

$(x+2y)(\frac{1}{5}+\frac{1}{3})$

$(x+2y)\times \frac{8}{15}$

$30\times\frac{8}{15} = 16$

Answer 1

$ \left( \dfrac{2y}{5}+\dfrac{x}{3}\right) + \left( \dfrac{x}{5}+\dfrac{2y}{3} \right)$

Taking LCM we get:

$\left(\dfrac{6y+5x+3x+10y}{15}\right)$

$ \left(\dfrac{8x+16y}{15}\right)$

$\left(\frac{8(x+2y)}{15}\right)= \dfrac{8\times 30}{15}=16$

Option B) is correct

Comments

 Ashwani Kumar 2 Taking 8 as common from expression $$(8x+16y)$$ so that it gives (x+2y ) whose value is given in the question.now expression become (8*30)/15 = 16.

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It just a typo mistake, now it is corrected!!

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Ya, that was typo.. thanks Lakshman for correcting

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No need to take LCM,we can just  look at the denominator 3 & 5 and add the corresponding numerators,we can easily then substitute the value 30 then  

Brackets are traps made diligently to kill one's time

Answer 2

Ans: b) 16

The brackets are summed.

The equation can be written as

$(\frac{2y}{5} + \frac{x}{3}) + (\frac{x}{5} + \frac{2y}{3}) = (\frac{x}{5} + \frac{2y}{5}) + (\frac{x}{3} + \frac{2y}{3}) = 30/5 + 30/3 = 16$

Answer 3

$\underline{\mathbf{Answer:}\Rightarrow}\;\mathbf{b.}$

Quick Trick: Look carefully there are $3$ and $5$ in the denominator.

Multiply $3$ and $5$, we get $15$.

Now, put $y = 15$ and $x =0$

Substitute in the equation and the answer will be $16$.

Answer 4

By observationwe see that 30 is consists of TWO parts. Both the will be divisible by 5 and 3 i,e by 15.

so by tricky observation let both part equal to 15 i.e x=15 and 2y=15 ,

then putting these two values in the given expression we evaluate and found 16.

Hence option B is the answer.