A sum of Rs 54,000 is divided among P, Q, R and S such that the ratio of the shares of P and Q is 2 : 3, that of Q and R is 4 : 5, and that of R and S is 3 : 2. What is the difference between the shares of Q and S?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Rs 2,400
To join the ratios, the common person must get the same number in both ratios: make Q the same in the first two, then R the same in the last two.
P : Q \(=2:3=8:12\) and Q : R \(=4:5=12:15\)
P : Q : R \(=8:12:15\)
R is 15 here and 3 in R : S, so R : S \(=3:2=15:10\)
P : Q : R : S \(=8:12:15:10\); total parts \(=45\)
One part \(\displaystyle =\frac{54000}{45}=\) Rs 1200
Q \(=12\times1200=\) Rs 14,400 and S \(=10\times1200=\) Rs 12,000
Difference \(=14400-12000=\) Rs 2,400
The shares of Q and S differ by Rs 2,400.