SSC CGL Maths · Time and Work

Efficiency Ratios

Efficiency is work done per day, so a worker who is k times as efficient takes one k-th of the time, and a ratio of times is a ratio of efficiencies turned upside down.

All Time and Work notes

Why this matters

Thirteen questions in the bank, six EASY and seven MODERATE, four of them from the 2025 shifts: one worker 40% more efficient than another, one working 3.5 times as fast and taking 45 days less, times given in a ratio. Giving each worker its efficiency as units a day turns every one of them into whole numbers in one line.

Concept 1 of 2: Efficiency ratio and time ratio

Twice as efficient means twice the work in a day, so the same job takes half as long. A ratio of efficiencies flips over to become the ratio of times.

Definition

Efficiency is the work done per day, the same thing as the rate.
Time is inversely proportional to efficiency: if the efficiencies are $p : q$ , the times are $q : p$ .
"x% more efficient" means the efficiencies are $(100 + x) : 100$ . Reduce it: 25% more is $5 : 4$ , 40% more is $7 : 5$ , 50% more is $3 : 2$ , 60% more is $8 : 5$ .
"k times as efficient" multiplies the rate by $k$ and divides the time by $k$ .
Fast route, units from efficiency: give each worker its efficiency in units a day. The whole job $=$ efficiency $\times$ own days for any one worker, and working together you add the efficiencies.

Efficiency and time

\frac{T_A}{T_B} = \frac{E_B}{E_A} \qquad \text{Work} = E \times T

$E_A, E_B$ efficiencies (work per day) of A and B
$T_A, T_B$ days each needs alone
E, Tone worker's efficiency and the days that worker needs

Worked example

A is 25% more efficient than B. B alone can finish a job in 30 days. How long do A and B take working together?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 14 Sep 2025, Shift 3 · Q64Easy

Example 1 · Time and Work · Efficiency Ratios

The ratio of the time taken by A and B to complete a task is

3 : 2

. If B can complete the task alone in 18 hours, how many hours will they take to complete the task if they work together?

Not flipping the ratio

If the efficiencies are

5 : 2

, the times are

2 : 5

, not

5 : 2

. The more efficient worker always takes less time.

Reading 60% more efficient as 60% less time

A worker 60% more efficient takes

\frac{100}{160} = \frac{5}{8}

of the time, a cut of 37.5%, not 60%.

Drill 8 more on efficiency ratio and time ratio

Concept 2 of 2: A faster worker who takes fewer days

If A is 3 times as fast as B, B needs 3 times A's days. The gap between their times is then 2 of A's times, and that pins down A's time.

Definition

If A works $k$ times as fast as B and takes $t$ days, B takes $kt$ days.
The gap is $kt - t = (k - 1)t$ . Set it equal to the stated difference $D$ : $t = \frac{D}{k - 1}$ .
Together they take $\frac{t \times kt}{t + kt} = \frac{kt}{k + 1}$ days.
Wording: SSC's keys read "k times more efficient" as $k$ times as efficient, although strictly the words mean $k + 1$ times. Solve with $k$ the way the key does, and look at the options before choosing.

Faster worker, fewer days

t = \frac{D}{k - 1} \qquad T_{\text{together}} = \frac{kt}{k + 1}

khow many times as fast A is as B
tdays A takes alone
Dhow many fewer days A takes than B

Worked example

A works 4 times as fast as B and takes 30 days less than B to finish a job. How long do they take working together?

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

SSC CGL · 2023 · Tier I, 21 Jul 2023, Shift 1 · Q68Moderate

Example 2 · Time and Work · Efficiency Ratios

A works 3.5 times as fast as B, and A takes 45 days less than B to complete a job when each works alone. Calculate the number of days taken to complete the same job if A and B work together.

Dividing the gap by k

If A is 3 times as fast as B and takes 40 days less, A's time is

\frac{40}{3 - 1} = 20

days, not

\frac{40}{3}

. The gap is

k - 1

of A's times.

Drill 3 more on a faster worker who takes fewer days

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Efficiency ratio and time ratio
Efficiency and time
$\frac{T_A}{T_B} = \frac{E_B}{E_A} \qquad \text{Work} = E \times T$
A faster worker who takes fewer days
Faster worker, fewer days
$t = \frac{D}{k - 1} \qquad T_{\text{together}} = \frac{kt}{k + 1}$

Watch out for (3)

Not flipping the ratio
→ Efficiency ratio and time ratio
Reading 60% more efficient as 60% less time
→ Efficiency ratio and time ratio
Dividing the gap by k
→ A faster worker who takes fewer days

Test yourself on Time and Work

20 past SSC CGL questions from this chapter, timed at 12 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

Take the Time and Work chapter test Drill all 13 questions