Two friends A and B went to fruit market to buy some fruits. At first shop B bought some mangoes at Rs. a per mango and A bought 9 mangoes more than B. At the next shop A bought some apples at a unit price of Rs. b per apple and B bought 18 apples more than A. Later, it was found that the ratio of number of fruits bought by A and B is 4: 7, respectively. whereas the amounts of money spent by them to buy fruits are the same. Find the ratio a: b.

Correct option is A

Given:
Money spent by A and B are same amount
Solution:
Let the number of mangoes bought by B from the first shop be x.
=> Then A buys (x + 9) mangoes from the same shop.
Let the number of apples bought by A from the second shop be y.
=> Then B buys (y + 18) apples from that shop.
A’s total fruits = Mangoes + Apples = (x + 9 + y)
B’s total fruits = Mangoes + Apples = (x + y + 18)
Let the price per mango = Rs. a and price per apple = Rs. b
A’s total expenditure = Cost of mangoes + Cost of apples = (x + 9) × a + y × b
B’s total expenditure = Cost of mangoes + Cost of apples = x × a + (y + 18) × b
Accordingly,
[(x + 9)a + by] = [ax + (y + 18)b]
=> ax + 9a + by = ax + by + 18b
=> 9a = 18b
=> a/b = 18/9
=> a : b = 2 : 1
∴ The required ratio of a : b = 2 : 1.