There are two numbers such that the sum of twice the first number and thrice the second number is 100 and the… · ABC26GN1692
Subject: General Aptitude · Chapter: Problems on Numbers
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? (Bank P.O., 2010)
(a)12
(b)14
(c)32
(d)35
(e)None of these
Answer
Answer (as printed): C
Explanation
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.
Explanation as extracted from the printed page; notation may be imperfect.