There are two numbers where 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 largest number?

Question: There are two numbers where 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 largest number?

Solution:
ধরি, প্রথম সংখ্যাটি x
এবং ২ য় সংখ্যাটি y

তাহলে,
2x + 3y = 100.....(1)
3x + 2y = 120.......(2)

(1) × 2 - (2) × 3 ⇒
4x + 6y - 9x - 6y = 200 - 360
⇒ - 5x = - 160
∴ x = 32

From (1) we get
2x + 3y = 100
⇒ 2 × 32 + 3y = 100
⇒ 64 + 3y = 100
⇒ 3y = 100 - 64
⇒ 3y = 36
∴ y = 12

অর্থাৎ, বড় সংখ্যাটি হচ্ছে 32.