Instructions

At the start of a game of cards, J and B together had four times as much money as T, while T and B together had three times as much as J. At the end of the evening, J and B together had three times as much money as T, while T and B together had twice as much as J. B lost Rs. 200

Solution

Let the initial amount with them be

J1 , B1 and T1

Now as per given

J1+B1 =4T1 (1)

T1+B1 = 3J1 (2)

Total amount with them will be 4J1 or 5T1

Now Let final amounts with them be J2 , B2 and T2 respectively .

J2 +B2 = 3T2 (3)

T2 +B2 = 2J2 (4)

Total amount with them will be 4T2 or 3J2

Now 5T1 =4T2 =4J1=3J2

From (1)

B1 = 4T1-J1

= 4T1-5/4 T1

= 11/4 T1

B2 = 3T2 -J2

=3T2 -4/3T2

=5/3 T2

5/3 (5/4) T1

= 25/12 T1

Now B1-B2 = 11/4 T1 -25/12T1 =200

so we get 8/12 T1 = 200

we get T1 = 300

so B1 = 11/4 (300) = 825

B2 = 25/12 (300) = 625

T2 = 5/4(300) = 375

J1 = 375

J2 = 4/3 (375) = 500

Total money = 825+375+300 =1500

Money T had with respect to total = 300/1500 = 1/5

**Alternative solution:**

It is given that the J and B had 4 times the money as T(in the beginning). Thus, if T had x amount with him, the total amount with them will be 5x.

So, let's assume that the total amount with them is 60x(LCM of 5, 4, and 3).

**In the beginning**: Now, the amount with T will be 12x, and the sum of the amount with J and B will be 48x.

Since the amount with T and B is 3 times that with J, the amount with J will be 15x. Thus, the amount with B will be 33x.

**At the end**: Since the amount with J and B is three times that of T, T will have 15x at the end. Also, the amount with T and B is twice that of J; the amount with J will be 20x. Thus, B will have 25x at the end.

Now, the ratio of money with T in the beginning with respect to the total amount = $$\frac{12x}{60x}=\frac{1}{5}$$

Thus, the correct option is D.

Create a FREE account and get:

- All Quant Formulas and shortcuts PDF
**170+**previous papers with solutions PDF- Top 5000+ MBA exam Solved Questions for Free

SNAP Averages, Ratio and Proportion QuestionsSNAP Quadratic Equations QuestionsSNAP Logarithms, Surds and Indices QuestionsSNAP Logarithms, Surds and Indices QuestionsSNAP Inequalities Questions

SNAP Logical Reasoning QuestionsSNAP Data Interpretation QuestionsSNAP Data Interpretation QuestionsSNAP Data Interpretation QuestionsSNAP Logical Reasoning Questions