Sharing sweets under two ratios

A bag of \(T\) sweets is shared among Ann, Bala and Chen. Plan 1 shares them in the ratio \(2:3:4\); Plan 2 shares them in the ratio \(3:4:5\).

1. Explain why \(T\) must be a multiple of \(36\) for both plans to give whole numbers of sweets.[2]
2. Chen receives \(6\) fewer sweets under Plan 2 than under Plan 1. Find \(T\).[3]
3. Show that Bala receives the same number of sweets under both plans, whatever the value of \(T\).[2]