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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let the original number of stamps Rani n Raja have be x and y respectively.
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
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
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