Question 9 SSC CGL 2018 June 4 Shift 1

Posted by Parveen(Hoven),
Aptitude Trainer and Software Developer

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Question 9 SSC-CGL 2018 June 4
[NOTE: only math questions solved]

Question: The ratio of efficiencies of A, B and C is 2: 5: 3. On working together, all three of them can complete work in 27 days. In how many days will both B and C together complete the 4/9th part of that work?

1. 15 days
2. 17-1/7
3. 27
4. 24

Method 1

Work that A+B+C can together do in 1 day is $\displaystyle 2k + 5k + 3k = 10k$.

Total work in 27 days = $\displaystyle 27 \times 10k = 270k$

Days taken by B+C to complete (5k + 3k) = 8k is = 1 days

$\displaystyle \therefore $ days to complete $\displaystyle \frac 49 \times 270k\text{ i.e., } 120k$ will be $\displaystyle \frac{1}{8k} \times 120k = 15$ days Ans.

Method 2

This is the classic, school math approach.

Total units of work are $\displaystyle 27$

Work to be done by B and C is $\displaystyle \frac 49 \times 27 = 12$ units

B + C can complete $\displaystyle \frac{5 + 3}{10} = \frac{4}{5}$ work in 1 day

Hence, they complete $\displaystyle 12$ units in $\displaystyle \frac{1}{4/5} \times 12 = 15$ days Ans.

Method 3

Use the principle that $\displaystyle \frac{M \times D}{W}$ is constant. M = number of men, D = days they work, and W is the fraction, or amount of work they do.

When A+B+C work together, $\displaystyle M_1 = 2k + 5k + 3k = 10k$, $\displaystyle D_1 = 27, W_1 = 1$

When B+C work together, $\displaystyle M_2 = 5k + 3k = 10k$, $\displaystyle D_2 = x, W_2 = \frac 49$

Now, $\displaystyle \frac{M_1 \times D_1}{W_1} = \frac{M_2 \times D_2}{W_2}$

Hence, $\displaystyle \frac{10k \times 27 }{1} = \frac{8k \times x}{\frac 49}$

Solving, $\displaystyle x = 15$ days, Ans.