The amount of money held by A, B, and C satisfy A:B = 3:4 and B:C = 5:6. If A gives Tk 5,000 to B, the ratio of their amount becomes 1:2. Find the…

Combine the ratios with B common: A : B = 3 : 4 = 15 : 20, and B : C = 5 : 6 = 20 : 24, so

\(A : B : C = 15 : 20 : 24\). Let A = 15k, B = 20k, C = 24k.

After A gives Tk 5,000 to B:

\(\dfrac{15k - 5000}{20k + 5000} = \dfrac{1}{2} \Rightarrow 30k - 10000 = 20k + 5000 \Rightarrow k = 1500\)

A = Tk 22,500, B = Tk 30,000, C = Tk 36,000. Check: 17,500 : 35,000 = 1 : 2.

Total originally = 59k = Tk 88,500.

— rhs