An amount of Rs.2430 is divided among A, B, C such that if their shares be reduced by Rs.5, Rs.10 and Rs.15 respectively, the remainders shall be in the ratio 3: 4: 5. The share of B isa) Rs 1015 b) Rs 810 c) Rs 605 d) Rs 595 Correct answer is option 'B'. Can you explain this answer?

Question

An amount of Rs.2430 is divided among A, B, C such that if their shares be reduced by Rs.5, Rs.10 and Rs.15 respectively, the remainders shall be in the ratio 3: 4: 5. The share of B isa)                                  Rs 1015                               b)                                  Rs 810                               c)                                  Rs 605                               d)                                  Rs 595                               Correct answer is option 'B'. Can you explain this answer?

Answer

Given:
Total amount = Rs.2430
Ratio of remainders after reducing shares by Rs.5, Rs.10, Rs.15 respectively = 3:4:5

Let the original shares of A, B, C be x, y, z respectively.
Then, we have:
x + y + z = 2430 --- (1)
(x-5)/(y-10) = 3/4 => 4x - 20 = 3y - 30 => 4x - 3y = -10 --- (2)
(y-10)/(z-15) = 4/5 => 5y - 50 = 4z - 60 => 5y - 4z = -10 --- (3)

Solving equations (2) and (3), we get:
x = 730, y = 1015, z = 1185

Therefore, the share of B = Rs.1015. Hence, option (b) is the correct answer.

Explanation:
To solve this question, we need to use the concept of ratios and equations in two variables. Let's break down the solution into steps:

Step 1: Let x, y, z be the original shares of A, B, C respectively. Then, we can write:
x + y + z = 2430 --- (1)
This equation represents the total amount given to A, B, C.

Step 2: According to the given condition, if their shares be reduced by Rs.5, Rs.10 and Rs.15 respectively, the remainders shall be in the ratio 3:4:5. This means:
(x-5)/(y-10) = 3/4
(y-10)/(z-15) = 4/5

Simplifying these equations, we get:
4x - 3y = -10 --- (2)
5y - 4z = -10 --- (3)

Step 3: We need to solve equations (1), (2) and (3) simultaneously to find the values of x, y and z. We can do this by using any suitable method, such as substitution or elimination.

Using elimination method, we can multiply equation (2) by 5 and equation (3) by 4, and then subtract them to eliminate y. This gives:
20x - 15y = -50
20y - 16z = -40
Subtracting these two equations, we get:
20x - 15y - 20y + 16z = -10
20x - 35y + 16z = -10

Now, we can substitute equation (1) into this equation to eliminate x. This gives:
20(2430 - y - z) - 35y + 16z = -10
48600 - 20y - 20z - 35y + 16z = -10
-55y - 4z = -48590

Finally, we can solve this equation and equation (3) simultaneously to find the values of y and z. Substituting z = 1185 - (5/4)y from equation (3) into the above equation, we get:
-55y - 4(1185 - (5/4)y) = -48590
-55y - 4740

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