Question

120 men working 9 hours a day can construct a road in 40 days.how long would it take to construct the same road if 150 men work 6 hours a day on it?
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Answer 1

Answer:

This is a question from Ratio and Proportion based concept.

Given that,

120 men working for 9 hours a day, construct a road in 40 days. We are required to calculate the number of days to construct the road if 150 people work for 6 hours.

Let's assume the number of days taken for constructing is 'x'.

So normally we take 2 ratios and obtain the unknown value by cross multiplication. Applying the same approach we get:

$\implies \dfrac{ 120\:men}{150\:men} = \dfrac{9\:hours}{6\:hours} = \dfrac{40\:days}{x\:days}$

Since the first two fractions are inversely related, we multiply the numerators and denominators respectively. Hence we get:

$\implies \dfrac{ 120\: men \times 9\: hours}{150\: men \times 6\: hours} = \dfrac{ 40\: days}{x\: days}\\\\\\\implies \dfrac{1080}{900} = \dfrac{40}{x}\\\\\\\text{Cross multiplying these 2 fractions we get:}\\\\\\\implies 1080 \times x = 40 \times 900 \\\\\\\implies x = \dfrac{ 40 \times 900}{1080}\\\\\\\implies x = \dfrac{36000}{1080}\\\\\\\implies x = \boxed{ 33.33 \:\: days}$

Hence it takes 33.33 days for 150 men to construct the road working for 6 hours each day.

Answer 2

Answer:

Given :-

120 men working 9 hours a day can construct a road in 40 days.

To Find :-

long would it take to construct the same road if 150 men work 6 hours a day on it?

Solution :-

Here,

Let the time be y

Men 1/Men 2 × Time 1/ Time 2 = Day 1/Day 2

120/150 = 9/6 = 40/y

120 × 9/150 × 6 = 40/y

1080/150 × 6 = 40/y

1080/900 = 40/y

By, Cross Multiplication

40 × 900 = 1080 × y

36,000 = 1080 × y

36,000 = 1080y

36,000/1080 = y

$\fbox {y = 33.33 \: days}$

Therefore,

33.33 days for 150 men to construct the road working for 6 hours each day.