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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 ?

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 ? Correct Answer 32

Let the numbers be x and y
Then,
2x + 3y = 100 ..... (i)
And,
3x + 2y = 120 ..... (ii)
Adding (i) and (ii), we get :
5x + 5y = 220
or x + y = 44 ..... (iii)
Subtracting (i) from (ii): we get :
x - y = 20 ..... (iv)
Adding (iii) and (iv), we get :
2x = 64
or x = 32
Putting x = 32 in (iii), we get :
y = 12
Hence, larger number = 32

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