Question

If A, B and C enter a partnership with shares in the ratio of \(\frac{4}{3} : \frac{7}{2} : \frac{6}{5}\) after 4 months, A increases his share by 108.75%. If the total profit in the end of one year is ₹17,208 then B's share in the profit is:

• A. ₹7,604
• B. ₹8,604
• C. ₹2,002
• D. ₹5,708

Hint:

Always simplify the ratio of fractions to integers first. When an investment changes, calculate the "Effective Capital" as \(\sum (\text{Investment} \times \text{Duration})\).

Answer 1

The Correct Option is B

Strategy:

The series is \(-0.25, 0.25, 0.75, \dots\) Check the common difference \(d\): \[ d = 0.25 - (-0.25) = 0.50 \] \[ d = 0.75 - 0.25 = 0.50 \] This is an Arithmetic Progression (AP) with first term \(a = -0.25\) and \(d = 0.5\).
The \(n^{\text{th}}\) term \(T_n\) is given by: \[ T_n = a + (n-1)d \] We are given \(T_n = 17.25\). \[ 17.25 = -0.25 + (n-1)(0.5) \]
Add 0.25 to both sides: \[ 17.50 = (n-1)(0.5) \] Divide by 0.5 (which is equivalent to multiplying by 2): \[ n - 1 = 17.5 \times 2 \] \[ n - 1 = 35 \] \[ n = 36 \] The term is the \(36^{\text{th}}\) term.