A and B each has some money. If A gives Rs 30 to B, then B will have t

1.	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?
Answer» Let the amount of money which A has be ’a’ and which B has be ‘b’. Given, If A gives Rs 30 to B, then B will have twice the money left with A. ⇒ b + 30 = 2(a – 30) ⇒ b + 30 = 2a – 60 ⇒ b = 2a - 60 - 30 ⇒ b = 2a – 90 --------- (1) But, if B gives Rs 10 to A, then A will have thrice as much as is left with B a + 10 = 3(b - 10)a+10 = 3b - 30a = 3b - 30 - 10 ⇒ a = 3b - 40 --------- (2) Substituting ‘a’ from eq2 in eq1b = 2(3b - 40) – 90 ⇒ b = 6b - 80 – 90 ⇒ b - 6b = - 80 – 90 ⇒ - 5b = -170 ⇒ b = -170/- 5 ⇒ b = Rs. 34 Substitute value of b in eq. 2, a = 3(34) - 40 Thus, a = 102 – 40 = Rs. 62 Hence, A has Rs 62 and B has Rs 34.

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?

Answer»

Let the amount of money which A has be ’a’ and which B has be ‘b’.

Given,

If A gives Rs 30 to B, then B will have twice the money left with A.

⇒ b + 30 = 2(a – 30)

⇒ b + 30 = 2a – 60

⇒ b = 2a - 60 - 30

⇒ b = 2a – 90 --------- (1)

But, if B gives Rs 10 to A, then A will have thrice as much as is left with B

a + 10 = 3(b - 10)a+10 = 3b - 30a = 3b - 30 - 10

⇒ a = 3b - 40 --------- (2)

Substituting ‘a’ from eq2 in eq1b

= 2(3b - 40) – 90

⇒ b = 6b - 80 – 90

⇒ b - 6b = - 80 – 90

⇒ - 5b = -170

⇒ b = -170/- 5

⇒ b = Rs. 34

Substitute value of b in eq. 2,

a = 3(34) - 40

Thus,

a = 102 – 40 = Rs. 62

Hence, A has Rs 62 and B has Rs 34.