A sum of money is to be distributed among P, Q and R in the ratio of 6:19:7. If R gives Rs. 200 from his share to Q, the ratio of P, Q and R becomes 3:10:3, what is the total sum?a)Rs. 3200b)Rs. 12800c)Rs. 6400d)data inadequateCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Given:
- The ratio of the money to be distributed among P, Q, and R is 6:19:7.
- When R gives Rs. 200 from his share to Q, the new ratio becomes 3:10:3.

To find:
The total sum of money.

Solution:
Let's assume the initial sum of money is x.

Step 1: Distributing the initial sum of money (x) in the ratio of 6:19:7.
- Share of P = (6/32) * x = 3x/16
- Share of Q = (19/32) * x = 19x/32
- Share of R = (7/32) * x = 7x/32

Step 2: When R gives Rs. 200 from his share to Q, the new ratio becomes 3:10:3.
- Share of P remains the same: 3x/16
- Share of Q = (19x/32) + 200
- Share of R = (7x/32) - 200

Step 3: Set up the equation based on the given ratios:
3x/16 : (19x/32) + 200 : (7x/32) - 200 = 3 : 10 : 3

Step 4: Simplify the equation:
3x/16 : (19x/32) + 200 : (7x/32) - 200 = 3/3 : 10/3 : 3/3
3x/16 : (19x/32) + 200 : (7x/32) - 200 = 1 : 10/3 : 1

Step 5: Cross-multiply and solve for x:
3x/16 = (19x/32) + 200
Multiply both sides by 16:
3x = 19x/2 + 3200
Multiply both sides by 2:
6x = 19x + 6400
13x = 6400
x = 6400/13

Step 6: Calculate the total sum of money:
Total sum = x = 6400/13 = 492.3077

Therefore, the total sum of money is approximately Rs. 6400. Hence, option (c) is the correct answer.

Similar Defence Doubts

A gentleman left a sum of Rs. 39000 to be distributed among his widow, 5 sons and 4 daughters. If each son receives three times as much as a daughter receives, and each daughter receives twice as much as their mother receives, then what is the widow’s share?

If a sum of money at a certain rate of simple interest per year doubles in 5 years and at a different rate of simple interest per year becomes three times in 12 years, then the difference in the two rates of simple interest per year is

The simple interest accrued on a sum of money at the end of four years is 1/5th of its principal. What is the rate of interest per annum?

A person distributes his pens among four friends A, B, C and D in the ratio 1/3 : 1 / 4 : 1/5 : 1/6. What is the minimum number of pens that the person should have ?

Rs. 120 is distributed among A, B and C so that A’s share is Rs. 20 more than B’s and Rs. 20 less than C’s. What is the B’s share?

Top Courses for Defence

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams