Unitary Method 1

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Problem 1: A can do a piece of work in 8 days and B in 12 days. After completing a piece of work, they get $ 120 as wages. How would they share the wages?

Solution 1: A takes 8 days and B takes 12 days to finish the work
Therefore, efficiency of A : Efficiency of B = 12 : 8 or 3: 2
Therefore, the wages have to be divided in the ratio 3 : 2
A will get (120 X 3) / 5 = $ 72 and
B will get (120 X 2)/5 = $ 48.

Problem 2: If 7/8 of a number is 7/2 more than 3/4 of the same number, what is the number?

Solution 2: The difference between 7/8 times of a number and 3/4 times of a number is 7/8 – 3/4 = 1/8 times of the number. 1/8 of the number is 7/2
Therefore, that number is 7/2 X 8 or 28.

Problem 3: A man bought a dress material for $ 2464. On coming home, he realized that that the dress material was shorter by 1/2 m than the required length. He was cheated by $ 224 on account of this loss. What was the actual length of the dress material purchased?

Solution 3: The man incurs a loss of $ 224 because of 1/2 m decrease of length of the dress material, i.e., 1/2 m of the dress material costs $ 224.
For $ 2464 he should have got 2464/(224 X 2) meters
i.e., 2464/(224 X 2) = 11 /2 meters
However, he got 1/2 meter less
Hence, the length of the dress material purchased is only 5 meters.