Such problem sums are also known as:
- Constant Total Concept
- Total Unchanged Quantities
- Internal Transfer (Unchanged Total) Concept
The important thing to note here is that the total remains the same, usually because transfer is internal. When external transfer is involved, it's always done in such a way that the total still remains unchanged.
TU1:
Raphael and Leonardo had the same number of stamps. After Raphael had given 80 stamps to Leonardo, Leonardo had twice as many stamps as Leonardo. How many stamps did Leonardo have in the end?Bala and Danny had money in the ratio 5 : 4. After Bala gave Danny $40, they had an equal amount of money. How much money did Danny have in the end?
Lucy had 2 boxes of sweets. After transferring 5⁄9 of the sweets in Box B to Box A, the ratio of the number of sweets in Box A to the number of sweets in Box B became 3 : 2. Find the ratio of the number of sweets in Box A to the number of sweets in Box B at first.
Helen is reading a book. The ratio of the number of pages she has read to the number of pages she has not read is 2:5. If she reads another 50 pages, the number of pages she has read will become 75% of the number of pages she has not read. How many pages are there in the book?
TU6:
The ratio of the number of stamps that Diana had to the number of stamps that Eileen had was 3:8. Eileen gave 60 stamps to Diana. After that, they had the same number of stamps. How many stamps had Diana at first?
TU7:
At first, Yeti had twice the number of laser guns that Zork had. Zork gave 4 guns to Yeti. Subsequently, Yeti had thrice the number of laser guns that Zork had. How many laser guns did Yeti have in the end?
The ratio of the number of chickens to the number of
ducks on a farm was 8:5 at first. The farmer bought some more ducks and sold
some of the chickens. In the end, the total number of chickens and ducks on the
farm was unchanged. If the number of ducks increased by 20%, what percentage of
the chickens were sold?
Peter had 2 aquariums. He transferred 9⁄17 of the fish in Aquarium A to Aquarium B. After that, the number of fish in Aquarium B was 1.5 times the number of fish in Aquarium A. What was the ratio of the number of fish in Aquarium A to the number of fish in Aquarium B at first?
Alison has thrice as many books as Lorna. How many books must Alison give to Lorna so that each of them would have 62 books?
