SSC GD Constable 5 Feb 2025 Shift 2 Paper

Section: Elementary Mathematics

Question : 45 of 80

Marks: +1, -0

To do a certain task, A and B work alternately on alternate days, with B starting on the first day. A alone can complete the task in 22 days. If the work is completed in

11\;{1}/{2}

days, then in how many days will B alone complete the

\;{3}/{4}

part of the original task?

Six days
Seven days
Nine days
Eight days

Validate

Solution:

Total Work

=

Time × Efficiency
Calculation:
Let total work

=

LCM

22=22

units (for easy calculation)
Efficiency of A=22 ÷

22=1

unit/day
Since A and B work alternately starting with B, in 11.5 days:
B works on Day:

1,3,5,7,9,11 ⟶ 6

full days
A works on Day:

2,4,6,8,10

, and 0.5 of Day

12 ⟶ 5.5

days
A's total work

=5.5 × 1=5.5

units
Remaining work

=22-5.5=16.5

units
This 16.5 units is done by

B

in 6 days

\;\text " ⇒ B's efficiency "\;=16.5 ÷ 6=2.75 \;\text " units\/day "\;

Now, we need to find the time taken by B alone to complete

3 \/ 4

of the original work:
3/4 of

22=16.5

units
⇒ Time

=16.5 ÷ 2.75=6

days

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