The average weight of A, B and C is 50 kgs. The weight of B is 20 kgs less than A's weight and 5 kgs more than C's weight. What will be the average weight of A, B, C and D, if D we... The average weight of A, B and C is 50 kgs. The weight of B is 20 kgs less than A's weight and 5 kgs more than C's weight. What will be the average weight of A, B, C and D, if D weighs 2 kgs more than C? Read more

Steps to Solve

1. Identify given information We know the average weight of A, B, and C is 50 kg. Therefore, we can establish the equation:
   $$ \frac{A + B + C}{3} = 50 $$
   Multiplying both sides by 3 gives:
   $$ A + B + C = 150 $$

2. Establish relationships based on the problem From the problem statement, we have the following relationships:

• Weight of B is 20 kg less than A:
  $$ B = A - 20 $$
• Weight of B is 5 kg more than C:
  $$ B = C + 5 $$

3. Substituting B in terms of A and C Substituting the first equation into the second gives:
   $$ A - 20 = C + 5 $$
   Rearranging this, we can express C in terms of A:
   $$ C = A - 25 $$

4. Substituting C back into the equation for A, B, C Now we substitute C back into the equation $ A + B + C = 150 $:
   $$ A + (A - 20) + (A - 25) = 150 $$
   Simplifying this gives:
   $$ 3A - 45 = 150 $$

5. Solving for A Adding 45 to both sides:
   $$ 3A = 195 $$
   Dividing by 3 gives:
   $$ A = 65 $$

6. Finding B and C Now we can find B and C using the established relationships:

• For B:
  $$ B = A - 20 = 65 - 20 = 45 $$
• For C:
  $$ C = A - 25 = 65 - 25 = 40 $$

7. Finding D's weight If D weighs 2 kg more than C:
   $$ D = C + 2 = 40 + 2 = 42 $$

8. Calculating the average weight of A, B, C, and D Now we can calculate the average weight:
   $$ \text{Average} = \frac{A + B + C + D}{4} = \frac{65 + 45 + 40 + 42}{4} $$
   Calculating the numerator:
   $$ 65 + 45 + 40 + 42 = 192 $$
   Thus, the average is:
   $$ \text{Average} = \frac{192}{4} = 48 $$