`A` and `B` each has some money. If `A` gives Rs 30 to `B` , then `B` will have twice the money left with `A` . But, if `B` gives Rs 10 to `A` , then `A` will have thrice as much as is left with `B` . How much money does each have?

Explanation

Suppose A and B have ₹ x and ₹ y respectively.
Case I When A gives ₹ 30 to B.
Then, money with A = ₹( x - 30 )
` therefore ( y + 30 ) = 2 ( x - 30 ) rArr 2 x - y = 90 " " ` … (i)
Case II When B gives ₹ 10 to A
Then, money with A = ₹ ( x + 10 )
and money with B = ₹( y - 10 )
` therefore (x + 10) = 3 ( y - 10 ) rArr x- 3y = - 40 " " `... (ii)
On multiplying (ii) by 2 and subtracting the result from (i), we get
` 5 y = 170 rArr y = ( 170)/( 5) = 34 `.
Putting `y = 34 ` in (i) , we get
` 2x - 4 = 90 rArr 2x = ( 90 + 34 ) = 124 rArr x= ( 124 ) /( 2 ) = 62`.
` therefore x = 62 and y = 34`
Hence, A has ₹ 62 and B has ₹ 34.