Robin and Robert have some money in the ratio 4 : 3. Robin gives Rs. p to Robert. Now, they have equal amounts of money. Robert spends Rs. q out of the money he has. Now, the ratio becomes 4 : 3. Find the ratio p : q.

Assume Robin has 4x and Robert has 3x initially; Robin gives Rs. p to Robert, making their amounts 4x minus p and 3x plus p. Since these amounts become equal, we equate them to find that 4x minus p equals 3x plus p, which simplifies to x equals 2p. Substituting 2p for x gives Robert a new amount of 5p before he spends Rs. q, leaving him with 5p minus q. The new ratio of their money becomes 4p divided by (5p minus q), which is set equal to 4 thirds; solving this proportion yields 12p equals 20p minus 4q, so 4q equals 8p and the ratio p to q is 4 to 7.

• Thanks
• Wrong explanation