GATE2017 EC-2: GA-8

Question

$1200$ men and $500$ women can build a bridge in $2$ weeks. $900$ men and $250$ women will take $3$ weeks to build the same bridge. How many men will be needed to build the bridge in one week?

• A. $3000$
• B. $3300$
• C. $3600$
• D. $3900$

Comments

(1200M+500W)*2 = (900M+250W)*3

250w = 300M 

W = 1.2 M 

NOW put in one of the eq   (1200M + 5008*1.2M)*2

3600 MEN 

 

Answer 1

Assume a man can build the bridge in $x$ weeks and, a woman can build the bridge in $y$ weeks
We get,

• $ \frac{1200}{x} + \frac{500}{y} = \frac{1}{2} \qquad \to (1)$
• $\frac{900}{x} + \frac{250}{y} = \frac{1}{3} \qquad \to(2)$

$2 \times(2) - (1) \implies \frac{600}{x} = \frac{1}{6} \implies x = 3600.$

Hence, Correct Answer is $C.$ 3600 Men

Answer 2

$1200\times 2\ M-W + 500 \times 2\ W-W=900 \times 3\ M-W + 250 \times 3\ W-W$

$5\ W-W =6\ M-W$

$1\ W=\dfrac{6M}{5}$

---

$1200\ M+500\ W=1200\ M+ 500\times \dfrac{6M}{5}=1800\ M$

$1800\ M\leftarrow 2W$

$?\leftarrow 1W$

$?=3600\ M$

$ans: C$