Question

A B C and D have got some money with them. If A gives 8 rs to B ,B will have as much as C has and A will have 3 rupees less then C has. Also if A takes 6 rupees from C, A will have twice as much money as D. If B and D together have 50 rs ,how much money does A and B have .?

Answer 1

Let A, B, C and D have

A = Rs. y

B = Rs. x

C = Rs. z

D = Rs. (50-x)

 

If A gives 8 rs to B, B will have as much as C has and A will have 3 rupees less then C has.

 

A = y - 8

B = x + 8

C = z

D = 50-x

 

So,

x + 8 = z ----- (i)

y – 8 = z – 3 ---- (ii)

 

Also if A takes 6 rupees from C, A will have twice as much money as D.

A = y + 6

B = x

C = z - 6

D = 50-x

So,

y + 6 = 2(50-x) = 100 – 2x

y = 100 – 2x ----- (iii)

 

We have 3 unknowns and three equations

x + 8 = z ----- (i)

y – 8 = z – 3 ---- (ii)

y = 100 – 2x ----- (iii)

From (i) and (ii)

y – 8 = x + 8  – 3

y = x + 13 ----- (iv)

 

From (iii) and (iv)

x + 13  = 100 – 2x

3x = 87

x = 29

y = x + 13

y = 29 + 13

y = 42

 

x + 8 = z ----- (i)

29 + 8 = z

 

z = 37

 

So;

A has Rs. 29

B has Rs. 42

Answer 2

Answer:Let the amount of B is 'x

Then, A = x+13

B=x

C=x+8

and D = x+192x+192

Now B+D = 50

x+x+192x+192

x=27

Therefore, A = x+13

A = 27+13=40

and C=x+8

C=27+8=35