Question

A has as much money as B & C together have. If B gives Rs. 5 to C then C will have 4 times that of B has but if A gives Rs. 11 to C then C will have 4.5 times of what A has. What is the sum with B?

Answer 1

Let the Money with B be : B

Let the Money with C be : C

Given : A has as much money as B & C together have

⇒ Money with A is : B + C

Given : If B gives Rs. 5 to C then C will have 4 times that of B has

⇒ C + 5 = 4(B - 5)

⇒ C = 4(B - 5) - 5

Given : If A gives Rs. 11 to C then C will have 4.5 times of what A has

⇒ C + 11 = 4.5(B + C - 11)

⇒ C + 11 = 4.5B + 4.5C - 49.5

⇒ 3.5C = 60.5 - 4.5B

Substituting C = 4(B - 5) - 5 in the above Equation, we get :

⇒ 3.5(4(B - 5) - 5) = 60.5 - 4.5B

⇒ 3.5(4B - 20 - 5) = 60.5 - 4.5B

⇒ 3.5(4B - 25) = 60.5 - 4.5B

⇒ 14B - 87.5 = 60.5 - 4.5B

⇒ 18.5B = 148

⇒ B = 8

⇒ The Sum with B is Rs. 8