There are two numbers such that the sum of twice the first number and thrice the second number is 100 and the sum of thrice the first number and twice the second number is 120. Which is the larger number ?

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Solution

The correct option is A 32
Let the numbers be x and y, where x > y
$∴ 2 x + 3 y = 100$ ...(i)
3x + 2y = 120 ...(ii)
From Eq. (ii) $\times 3$ - Eq. $(i) \times 2,$ we have
9x + 6y - 4x - 6y = 360-200
$\Rightarrow 5 x = 160$
$∴ x = \frac{160}{5} = 32$

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There are two numbers such that the sum of twice the first number and thrice the second number is 100 and the sum of thrice the first number and twice the second number is 120. Which is the larger number ?

The correct option is A 32Let the numbers be x and y, where x > y ∴2x+3y=100 ...(i) 3x + 2y = 120 ...(ii) From Eq. (ii) ×3 - Eq. (i)×2, we have 9x + 6y - 4x - 6y = 360-200 ⇒5x=160 ∴x=1605=32

The correct option is A 32
Let the numbers be x and y, where x > y
$∴ 2 x + 3 y = 100$ ...(i)
3x + 2y = 120 ...(ii)
From Eq. (ii) $\times 3$ - Eq. $(i) \times 2,$ we have
9x + 6y - 4x - 6y = 360-200
$\Rightarrow 5 x = 160$
$∴ x = \frac{160}{5} = 32$