Time and Work - 03

Explanation:-

Let X litres be the per day filling and L litres be the capacity of the reservoir, then
90X + L = 40000 × 90 ----------- (1)
60X + L = 32000 × 60 ----------- (2)
Solving the equation,
X = 56000 litres
Thus, 56000 litres per day can be used without the failure of supply.

Explanation:-

Let initially X number of workers be there.
Now, Using work equivalence method,
X + (X - 1) + (X - 2) + . . . . . + 1 = X × 55% of X
$$\frac{{{\text{X}} \times \left( {{\text{X}} + 1} \right)}}{2} = \frac{{5{\text{X}}}}{{100}}$$
[series is in AP. Sum of AP = {No. of terms (first term + last term)/2}]
X = 10 workers.

Explanation:-

Let X be the initial number of men then,
According to the question,
4X = X + (X - 20) + (X - 40) + (X - 60) + (X - 80) + (X - 100) + (X - 120)
⇒ 4X = 7X - 420
⇒ 3X = 420
⇒ X = $$\frac{{420}}{3}$$
⇒ X = 140 men

Explanation:-

Mango Packing rate of Ram Lal = $$\frac{{70}}{7}$$ = 10 per hour
Guavas Packing rate of Ram Lal = $$\frac{{56}}{7}$$ = 8 per hour
Mango Packing rate of Ram Lal's Wife = $$\frac{{30}}{6}$$ = 5 per hour
Guavas Packing rate of Ram Lal's Wife = $$\frac{{24}}{6}$$ = 4 per hour

On comparing,
8 Guavas = 10 Mangoes
1 Guavas = $$\frac{{10}}{8}$$ Mangoes
2400 Guavas = $$\frac{{10 \times 2400}}{8}$$   = 3000 Mangoes
This means that they need to pack (6300 + 3000) Mangoes

Combined Mango Packing rate of Both = 10 + 5 = 15 per hour

We will take 2 days = 1 time unit.
Working 10 hours a day they will pack 150 Mangoes in 1 time unit
Total time taken to pack 6300 Mangoes = $$\frac{{6300}}{{150}}$$   = 42 time unit
So, total time taken = 2 × 42 = 84 days

Explanation:-

Time × Rate = total charges
100 × 100 = 10000
X × 125 = 110 [25% increase in rate, user can afford only 10% increase]
X = $$\frac{{110}}{{125}} \times 100$$   = 88%
Thus, decrease in time = 12%

Explanation:-

Let First division have x hectare of the land then second division will have (x - 12) hectare of land
Now according to the question,
25 × (x - 12) = 21x + 300
or, x = 150 hectare
Hence, the first division harvest 3150 tons tendu leaves.

Explanation:-

Working efficiency of both typist together,
= $$\frac{{100}}{6}$$ = 16.66% per minute

Now, let work efficiency of first typist be x and then second typist will be (16.66 - x)
First typist typed alone for 4 minutes and second typed alone for 6 minutes and they left with $$\frac{1}{5}$$ (i.e 20%) of job, means they have completed 80% job
Now,
First Typist typed in 4 minute + Second typed in 6 minutes = 80%
4 × x + 6 × (16.66 - x) = 80%
4x + 100% - 6x = 80%
x = 10%
First Typist typed 10% per minutes. Then second typed (16.66 - 10) = 6.66% per minute
Then, Second typist complete the whole job in $$\frac{{100}}{{6.66}}$$ = 15.01 = 15 minutes.

Explanation:-

X completes $$\frac{1}{3}$$ rd in 4 days = 33.33% job in 4 days
X One day work = 8.33%
Y one day work = 5.55% [As he complete $$\frac{1}{6}$$ job = 16.66% job in 3 days]
Z one day work = 10%
Work done in 3 days by X, Y and Z
= 25 + 16.66 + 30 = 71.66%
Remaining work will be done by Y in,
$$\frac{{28.33}}{{5.55}}$$   = 5.1 days

Explanation:-

M₁ × D₁ = M₂ × D₂
mr = (m +n) × D₂
D₂ = $$\frac{{{\text{mr}}}}{{{\text{m}} + {\text{n}}}}$$

Explanation:-

Efficiency of pipe A,
$$\frac{{100}}{{20}}$$ = 5%
20% of efficiency of A = 1%
Then, efficiency of 5 such pipes = 5%.
Then,
Time taken to fill the tank = $$\frac{{100}}{5}$$ = 20 min.