54 is divided into 2 parts such that sum of 10 times the first part and 22 times the second part is 780. The larger part is

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Solution

The correct option is A
34

Let the two parts be $x, y$

$\Rightarrow x + y = 54$ ...(1)

Also, $10 x + 22 y = 780$

$\Rightarrow 5 x + 11 y = 390$ ...(2)

Multiplying (1) by 5, we get

$5 x + 5 y = 270$ ...(3)

Subtracting (3) from (2),

$6 y = 120 \Rightarrow y = 20$

$∴, x = 54 - 20 = 34$

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54 is divided into 2 parts such that sum of 10 times the first part and 22 times the second part is 780. The larger part is

The correct option is A 34 Let the two parts be x,y ⇒x+y=54 ...(1) Also, 10x+22y=780 ⇒5x+11y=390 ...(2) Multiplying (1) by 5, we get 5x+5y=270 ...(3) Subtracting (3) from (2), 6y=120⇒y=20 ∴,x=54−20=34

The correct option is A
34

Let the two parts be $x, y$

$\Rightarrow x + y = 54$ ...(1)

Also, $10 x + 22 y = 780$

$\Rightarrow 5 x + 11 y = 390$ ...(2)

Multiplying (1) by 5, we get

$5 x + 5 y = 270$ ...(3)

Subtracting (3) from (2),

$6 y = 120 \Rightarrow y = 20$

$∴, x = 54 - 20 = 34$