PYQ Vault

CDS Mathematics · Formula sheet

Time and Work formulas

5 formulas and 7 common traps for CDS Mathematics Time and Work, grouped by subtopic.

Full notes with worked examples

Work Rates

Learn this subtopic in the notes

Adding and subtracting rates

Together

1T=1a+1b\dfrac{1}{T} = \dfrac1a + \dfrac1b

Joining, leaving and taking turns

Stages

r1t1+r2t2=1r_1 t_1 + r_2 t_2 = 1

Common traps

Times do not add

Workers taking 66 and 1010 hours do not finish together in 88 or 1616. Add the rates: 16+110=415\tfrac16 + \tfrac1{10} = \tfrac4{15}, so 3343\tfrac34 hours.

Pay by rate, not by time

The faster worker earns MORE for a joint job. Times xx, 1.5x1.5x, 2x2x give pay 6:4:36 : 4 : 3, the reverse of 2:3:42 : 3 : 4.

The last turn may be partial

Taking turns, the job often ends part-way through a day. Count the fraction left after the whole cycles and give that to the NEXT person, not to whoever would suit the answer.

Man-Days and Man-Hours

Learn this subtopic in the notes

Men × days × hours

Constant work

M1D1H1W1=M2D2H2W2\dfrac{M_1 D_1 H_1}{W_1} = \dfrac{M_2 D_2 H_2}{W_2}

Common traps

Count the whole job, not the part

If a quarter took 10,00010{,}000 man-days, the job is 40,00040{,}000 and the part LEFT is 30,00030{,}000. Sharing 40,00040{,}000 over the days left overstates the men needed.

Additional men, or men in all?

The calculation gives the number of men who must be working. Subtract the men already there when the question asks for ADDITIONAL men.

Men, Women and Equivalent Workers

Learn this subtopic in the notes

Rates of different workers

Two gangs, same job

d1(a1M+b1W)=d2(a2M+b2W)d_1(a_1M + b_1W) = d_2(a_2M + b_2W)

Common traps

OR is not AND

'88 men or 1212 women in 2424 days' means each group ALONE takes 2424 days. Together they take 1212, not 2424.

Pipes and Cisterns

Learn this subtopic in the notes

Inlets, outlets and leaks

Net rate

1T=1n−1m\dfrac1T = \dfrac1{n} - \dfrac1{m}

Common traps

Subtract the outlet

An outlet works AGAINST the tap. A tap of 44 hours and a leak of 1212 hours together take 66 hours, not the 33 hours that adding the rates would give.

More CDS Mathematics formula sheets