There are three boxes – P, Q and R, containing marbles in the ratio 1 : 2 : 3. Total number of marbles is 60. The above ratio can be changed to 3 : 4 : 5 by transferring :

1. 2 marbles from P to Q and 1 from R to Q

2. 3 marbles from Q to R

3. 4 marbles from R to Q

4. 5 marbles from R to P

Given,

Initial ratio,

P : Q : R = 1 : 2 : 3

Let initial no. of marbles in P, Q and R be x, 2x and 3x respectively.

Total number of marbles = 60.

⇒ x + 2x + 3x = 60

⇒ 6x = 60

⇒ x = $\dfrac{60}{6}$

⇒ x = 10

P = 1 × 10 = 10, Q = 2 × 10 = 20, R = 3 × 10 = 30.

Given,

New ratio of marbles = 3 : 4 : 5.

Let now the no. of marbles in box P, Q and R be 3x, 4x and 5x respectively.

⇒ 3x + 4x + 5x = 60

⇒ 12x = 60

⇒ x = $\dfrac{60}{12}$ = 5.

P = 3 × 5 = 15, Q = 4 × 5 = 20, R = 5 × 5 = 25.

Thus, if initially 5 marbles are transferred from R to P then the ratio changes from 1 : 2 : 3 to 3 : 4 : 5.

Hence, option 4 is the correct option.