GATE2018 ME-1: GA-3

Question

Seven machines take $7$ minutes to make $7$ identical toys. At the same rate, how many minutes would it take for $100$ machine to make $100$ toys?

• A. $1$
• B. $7$
• C. $100$
• D. $700$

Answer 1

Rate of work of a machine $ = \dfrac{7}{7 \times 7} = \dfrac{1}{7}$ toys per minute

With $100$ machines to make $100$ toys we need $\dfrac{100}{100 \times \text{Rate of work of a machine}} \text{ minutes}$

$\qquad =\dfrac{1}{\dfrac{1}{7}} = 7 \text{ minutes}$

Answer 2

$\dfrac{DMTE}{W}=C$(Constant)

Where, $D=$ Days, $M =$ Man Power/machines, $T =$ Time , $E =$ Efficiency, $W =$ Work

So, $\dfrac{M_{1}T_{1}}{W_{1}}=\dfrac{M_{2}T_{2}}{W_{2}}$

$\implies \dfrac{7\times 7}{7}=\dfrac{100\times T_{2}}{100}$

$\implies T_{2}=7$ minutes

So, the correct answer is $(B).$

Comments

best soln

Answer 3

Let work per minute be w.

Total Output=number of machines* number of minutes*work per minute.

Therefore,

For 1st case,7=7*7*w

This implies,w=1/7

For 2nd case, let x be the number of minutes needed to build 100 toys.

100=100*x*w

1=x/7

This implies number of minutes needed =x=7

Answer 4

Can be done by logic 

m/c → machine

7 min , 100 m/c can make 100 toys