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

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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