SSC CGL Tier1 Quantitative Aptitude Time and Work Test 6

Suppose A, B and C take $ x $,$\dfrac{x}{2}$ and $\frac{x}{3}$ days respectively to finish the work.

Then,$ \left(\dfrac{1}{x} +\dfrac{2}{x} +\dfrac{3}{x} \right) $=$ \dfrac{1}{2} $

$\Rightarrow \dfrac{6}{x} $=$ \dfrac{1}{2} $

$\Rightarrow x $ = 12.

So, B takes $\left(12/2\right)$ = 6 days to finish the work.

Ratio of times taken by A and B = 100 : 130 = 10 : 13.

Suppose B takes $ x $ days to do the work.

Then, 10 : 13 :: 23 : $ x $

        x =$ \left(\dfrac{23 \times 13}{10} \right) $

        x=$ \dfrac{299}{10} $.

As 1 days work =$ \dfrac{1}{23} $;

Bs 1 days work =$ \dfrac{10}{299} $.

$\left(A + B\right)$s 1 days work =$ \left(\dfrac{1}{23} +\dfrac{10}{299} \right) $=$ \dfrac{23}{299} $=$ \dfrac{1}{13} $.

Therefore, A and B together can complete the work in 13 days.

Cs 1 days work =$ \dfrac{1}{3} $-$ \left(\dfrac{1}{6} +\dfrac{1}{8} \right) $=$ \dfrac{1}{3} $-$ \dfrac{7}{24} $=$ \dfrac{1}{24} $.

As wages : Bs wages : Cs wages =$ \dfrac{1}{6} $:$ \dfrac{1}{8} $:$ \dfrac{1}{24} $= 4 : 3 : 1.

$\therefore$Cs share [for 3 days] = Rs.$ \left(3 \times\dfrac{1}{24} \times 3200\right) $= Rs. 400.

$\left(A + B + C\right)$s 1 days work =$ \dfrac{1}{4} $,

As 1 days work =$ \dfrac{1}{16} $,

Bs 1 days work =$ \dfrac{1}{12} $.

Cs 1 days work =$ \dfrac{1}{4} $-$ \left(\dfrac{1}{16} +\dfrac{1}{12} \right) $=$ \dfrac{1}{4}-\dfrac{7}{48}$=$ \dfrac{5}{48} $.

So, C alone can do the work in$ \dfrac{48}{5} $= 9$ \dfrac{3}{5} $days.

As 2 days work =$ \left(\dfrac{1}{20} \times 2\right) $=$ \dfrac{1}{10} $.

$\left(A + B + C\right)$s 1 days work =$ \left(\dfrac{1}{20} +\dfrac{1}{30} +\dfrac{1}{60} \right) $=$ \dfrac{6}{60} $=$ \dfrac{1}{10} $.

Work done in 3 days =$ \left(\dfrac{1}{10} +\dfrac{1}{10} \right) $=$ \dfrac{1}{5} $.

Now,$ \dfrac{1}{5} $work is done in 3 days.

$\therefore$ Whole work will be done in $\left(3 \times 5\right)$ = 15 days.

Amount Earned by P,Q and R in 1 day = 1620/9 = 180 ---[1]

Amount Earned by P and R in 1 day = 600/5 = 120 ---[2]

Amount Earned by Q and R in 1 day = 910/7 = 130 ---[3]

$\left(2\right)$+$\left(3\right)$-$\left(1\right)$ => Amount Earned by P , Q and 2R in 1 day

Amount Earned by P,Q and R in 1 day = $\left(120+130\right)$-180 = 70

=>Amount Earned by R in 1 day = 70

$\left(A + B\right)$s 1 days work =$ \dfrac{1}{10} $

Cs 1 days work =$ \dfrac{1}{50} $

$\left(A + B + C\right)$s 1 days work =$ \left(\dfrac{1}{10} +\dfrac{1}{50} \right) $=$ \dfrac{6}{50} $=$ \dfrac{3}{25} $. .... [i]

As 1 days work = $\left(B + C\right)$s 1 days work .... [ii]

From [i] and [ii], we get: 2 $\times $[As 1 days work] =$ \dfrac{3}{25} $

$\Rightarrow$ As 1 days work =$ \dfrac{3}{50} $.

$\therefore$ Bs 1 days work$ \left(\dfrac{1}{10} -\dfrac{3}{50} \right) $=$ \dfrac{2}{50} $=$ \dfrac{1}{25} $.

So, B alone could do the work in 25 days.

2$\left(A + B + C\right)$s 1 days work =$ \left(\dfrac{1}{30} +\dfrac{1}{24} +\dfrac{1}{20} \right) $=$ \dfrac{15}{120} $=$ \dfrac{1}{8} $.

Therefore, $\left(A + B + C\right)$s 1 days work =$ \dfrac{1}{2 \times 8} $=$ \dfrac{1}{16} $.

Work done by A, B, C in 10 days =$ \dfrac{10}{16} $=$ \dfrac{5}{8} $.

Remaining work =$ \left(1 -\dfrac{5}{8} \right) $=$ \dfrac{3}{8} $.

As 1 days work =$ \left(\dfrac{1}{16} -\dfrac{1}{24} \right) $=$ \dfrac{1}{48} $.

Now,$ \dfrac{1}{48} $work is done by A in 1 day.

So,$ \dfrac{3}{8} $work will be done by A in 48$ \times \dfrac{3}{8} $= 18 days.

Let As 1 days work = $ x $ and Bs 1 days work = $ y $.

Then, $ x $ + $ y $ =$ \dfrac{1}{30} $and 16$ x $ + 44$ y $ = 1.

Solving these two equations, we get: $ x $ =$ \dfrac{1}{60} $and $ y $ =$ \dfrac{1}{60} $

$\therefore$ Bs 1 days work =$ \dfrac{1}{60} $.

Hence, B alone shall finish the whole work in 60 days.

Work done by X in 4 days =$ \left(\dfrac{1}{20} \times 4\right) $=$ \dfrac{1}{5} $.

Remaining work =$ \left(1 -\dfrac{1}{5} \right) $=$ \dfrac{4}{5} $.

$\left(X + Y\right)$s 1 days work =$ \left(\dfrac{1}{20} +\dfrac{1}{12} \right) $=$ \dfrac{8}{60} $=$ \dfrac{2}{15} $.

Now,$ \dfrac{2}{15} $work is done by X and Y in 1 day.

So,$ \dfrac{4}{5} $work will be done by X and Y in $\left(\dfrac{15}{2}\times\dfrac{4}{5}\right) $= 6 days.

Hence, total time taken = $\left(6 + 4\right)$ days = 10 days.