The number of fruits in baskets A and B are in the ratio 7 : 9. If six fruits…

When two quantities are given in the ratio a : b, write them as ax and bx for a common multiplier x. If a fixed amount is then transferred from one quantity to the other, the new amounts form a new ratio — this gives one linear equation in x that fixes the multiplier and, with it, every quantity in the problem.

1. Let the fruits in basket A and basket B initially be 7x and 9x respectively, so the total is 16x.

2. After six fruits move from A to B, basket A holds 7x minus 6 fruits and basket B holds 9x plus 6 fruits.

3. The problem states this new split is in the ratio 1 : 3, so (7x minus 6) is to (9x plus 6) as 1 is to 3.

4. Cross-multiplying gives 3 times (7x minus 6) equals 9x plus 6, that is, 21x minus 18 equals 9x plus 6.

5. Collecting the x terms: 21x minus 9x equals 6 plus 18, so 12x equals 24, giving x equals 2.

6. The total number of fruits, 16x, therefore works out to 16 times 2 equals 32.

Checking this back: with x equal to 2, basket A starts with 14 fruits and basket B with 18, which is indeed in the ratio 7 : 9. Moving six fruits gives 8 and 24, and 8 : 24 reduces to 1 : 3, matching the stated condition exactly, confirming the total of 32 fruits.