1.

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»

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 Chas 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 havetwice 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


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