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Three times a number is 20% more than twice another number when increased by 105. If twice the first number is increased by 36 then it is 20% less than three times of the second number, then what is the first number?

Three times a number is 20% more than twice another number when increased by 105. If twice the first number is increased by 36 then it is 20% less than three times of the second number, then what is the first number?
1). 160
2). 161
3). 162
4). 163

This Question has 1 answers.

Let first number be ‘x’ and another number be ‘y’,

Now, three times a number is 20% more than twice another number when increased by 105,

⇒ 3x = (1 + 20%) × (2y + 105)

⇒ 3x = (6/5) × (2y + 105)

⇒ 5x = 4y + 210     ---- 1

Also, if twice the first number is increased by 36 then it is 20% less than three times of the second number,

⇒ 2x + 36 = (1 – 20%) × 3y

⇒ x + 18 = (2/5) × 3y

⇒ 5x + 90 = 6y     ---- 2

On solving equation 1 and 2,

⇒ x = 162 and y = 150

∴ First number, x = 162

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