In a school there are two sections A and B. When a few students from

Solution

• In a school there are two sections A and B.
• When a few students from section B took transfer to section A the strength of section A increased by 22.5% and strength of B decreased by 30%

• Now, what percentage of students in section A should be given a transfer to section B such that section A and section B have the same strengths

• Let the strength of sections A and B be A and B respectively
• If x students take transfer, then the new strengths will be A + x and B - x

• A + x = 1.225A, and
• B – x = 0.7B
• Solving two equations, we get, \(A = \frac{4B}{3}\)

o Implies, \(1.225A = \frac{49A}{40} = \frac{49B}{30}\), and
o \(0.7B = \frac{7B}{10}\)

• \(\frac{49B}{30} – y = \frac{7B}{10} + y\)
o Implies, \(y = \frac{7B}{15}\)