Question

Solve this question of Direct and Inverse variation.

A can make a wooden cupboard alone in 15 days, while B alone can complete in 12 days. They worked together for 3 days and then B leaves. In how many days will A finish the remaining work.

Answer 1

Solution:-

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ANSWER:-

• A will complete the work in $\tt{8\dfrac{1}{4}}$ days after B leaves.

GIVEN:-

• Time taken by A to complete a wooden cupboard = 15 days
• Time taken by B to complete a wooden cupboard = 12 days
• Time they worked together = 3 days

TO FIND:-

• In how many days will A finish the remaining work = ?

SOLVING STEP BY STEP:-

• Work done by A in a day = 1/15
• Work done by B in a day = 1/12
• Sum of the work both do in a day = 1/15 + 1/12
• (1/15) + (1/12)
• LCM of 15 and 12 is 60.
• (4 + 5)/60
• (4 + 5)/60 = 9/60
• So, A and B together do 9/60 of the total work in a day.
• Sum of the work both do in 3 days = (9/60) × 3
• (9/60) × 3
• Cancel 60 by 3.
• 9/20
• So, A and B together do 9/20 of the total work in 3 days.
• After that B left:-
• Work remains = (1 - 9)/20
• LCM is 20
• (20 - 9)/20
• (20 - 9)/20 = 11/20
• Work remains is 11/20 of the whole work.
• A alone will finish the work in days = (11/20) × 15
• (11/20) × 15
• Cancel 20 and 15
• (11/4) × 3
• (11/4) × 3 = 33/4
• 33/4 = $\tt{8\dfrac{1}{4}}$
• $\tt{8\dfrac{1}{4}}$ days.
• So, A will complete the work in $\tt{8\dfrac{1}{4}}$ days after B leaves.

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