There are two numbers where the sum of twice the first number and thrice the second number is 100. Again the sum of thrice the first number and twice the second number is 120. Which is the largest number?
Solution
Correct Answer: Option A
মনেকরি, সংখ্যাদ্বয় = x ও y
প্রশ্নমতে, 2x + 3y = 100 ........ (i)
3x + 2y = 120 ........ (ii)
(i) × 2 - (ii) × 3 ⇒
4x + 6y = 200
9x + 6y = 360
-5x = -160
⇒ x = 32
∴ (i) ⇒
2 × 32 + 3y = 100
⇒ 64 + 3y = 100
⇒ 3y = 100 - 64
⇒ 3y = 36
⇒ y = 12
∴ বড় সংখ্যাটি = 32
প্রশ্নমতে, 2x + 3y = 100 ........ (i)
3x + 2y = 120 ........ (ii)
(i) × 2 - (ii) × 3 ⇒
4x + 6y = 200
9x + 6y = 360
-5x = -160
⇒ x = 32
∴ (i) ⇒
2 × 32 + 3y = 100
⇒ 64 + 3y = 100
⇒ 3y = 100 - 64
⇒ 3y = 36
⇒ y = 12
∴ বড় সংখ্যাটি = 32
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