Salary Problem!

Number Theory Level pending

Four people A, B, C and D have an average monthly salary of $10000.The first three of them have an average monthly salary of $12000. The average salary of the first two is $15000. Find the individual monthly salaries of B, C and D if A has a monthly salary of $20000.

Type the answer in this order: BCD.


The answer is 1000060004000.

Soha Farhin Pine Pine by Soha Farhin Pine Pine , 18, Bangladesh

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1 solution

Average of A A , B B , C C , and D D 's salaries = $ 10000 \$10000

We know,

Average = sum of elements ÷ # of elements \textbf{Average = sum of elements} \div \textbf{\# of elements}

∴ A + B + C + D \therefore A + B + C + D = $ ( 10000 × 4 ) \$(10000\times 4) = $ 40000 \$40000 ——— (1)

Average of A A , B B , C C = $ 12000 \$12000

∴ A + B + C \therefore A + B + C = $ ( 12000 × 3 ) \$(12000\times 3) = $ 36000 \$36000 ——— (2)

Average of A A and B B 's salaries = $ 15000 \$15000

∴ A + B \therefore A + B = $ ( 15000 × 2 ) \$(15000\times 2) = $ 30000 \$30000 ——— (3)

A A 's salary = $ 20000 \$20000 ——— (4)

Insert (4) into (3):

B B 's salary = $ ( 30000 − 20000 ) \$(30000-20000) = $ 10000 \$\boxed{10000}

Insert (3) into (2):

C C 's salary = $ ( 36000 − 30000 ) \$(36000-30000) = $ 6000 \$\boxed{6000}

Insert (2) into (1):

D D 's salary = $ ( 40000 − 36000 ) \$(40000-36000) = $ 4000 \$\boxed{4000}

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