# Rani and Raja collected some stamps in the ratio 1 : 2. When Rani received 35 stamps from Raja, the ratio of the number of Rani`s stamps to Raja`s stamps became 4 : 3. How many stamps did they have altogether?

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acc+. to the 1st condition;

x/y=1/2

therefore 2x=y

therefore 2x-y=0-----(i)

acc. to the 2nd condition;

x+35/y-35=4/3

therefore (x+35)3=(y-35)4

therefore 3x+105=4y-140

therefore 3x-4y=-245---(ii)

multiplying (i) by 4;

8x-4y=0---(iii)

subtracting (ii) from (iii);

8x-4y=0

3x-4y=-245

(-) (+) (+)

-------------------

5x = 245

x=49

therefore Rani has 49 stamps

therfore Raja has 2(49)stamps(from eqn (i))=98stamps

therefore both of them had 98+49=147stamps altogether