Numerical Applications Test 28

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Numerical Applications Test 28

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Question 1
1 / -0

A booster pump can be used for filling as well as emptying a tank. The capacity of the tank is $$2400$$ $$\displaystyle m^{3}$$. The emptying capacity of the tank is 10$$\displaystyle m^{3}$$/min higher than its filling capacity and the pump needs 8 min lesser to empty the tank than it need to fill it. What is the filling capacity of the pump?

A
$$50$$ $$\displaystyle m^{3}/min.$$

B
$$60$$ $$\displaystyle m^{3}/min.$$

C
$$72$$ $$\displaystyle m^{3}/min.$$

D
None of these

Solution

Let the filled capacity of the tank $$x \ m^3/minute$$
Then emptied capacity of the tank$$=(x+10) \ m^3/minute$$
$$\therefore \dfrac{2400}{x}-\dfrac{2400}{x+10}=8$$
$$\Rightarrow 2400\left(\dfrac{10}{x(x+10)} \right)=8$$
$$\Rightarrow x(x+10)=3000$$
$$\Rightarrow x=50 \ m^3/min$$
Question 2
1 / -0

Pipes A and B can fill a tank in $$5$$ and $$6$$ hours respectively. Pipe C can empty it in $$12$$ hours. If all the three pipes are opened together then the tank will be filled in

A
$$\displaystyle 1\frac{13}{17}$$ hours

B
$$\displaystyle 2\frac{8}{11}$$ hours

C
$$\displaystyle 3\frac{9}{17}$$ hours

D
$$\displaystyle 4\frac{1}{2}$$ hours

Solution

Part filled by $$A$$ in $$1$$ hour $$=\dfrac{1}{5}$$
Part filled by $$B$$ in $$1$$ hour $$=\dfrac1{6}$$
Part emptied by $$C$$ in $$1$$ hour $$=\dfrac1{12}$$;
Part filled by $$(A + B-C)$$ in $$1$$ hour $$=\dfrac1{5}+\dfrac1{6}-\dfrac1{12}=\dfrac{17}{60}$$
Hence, three pipes together will fill the tank in $$3\dfrac{9}{17}$$ hours.
Question 3
1 / -0

$$A$$ takes twice as much time as $$B$$ or thrice as much time as $$C$$ to finish a piece of work. Working together, they can finish the work in $$2$$ days. $$B$$ can do the work alone in

A
$$3$$ days

B
$$7$$ days

C
$$4$$ days

D
$$6$$ days

Solution

Suppose $$A, B$$ and $$C$$ take $$x\,,\,\dfrac{x}{2}\,\,$$ and $$\dfrac{x}{3}$$ days respectively to finish the work.
Then, $$\left (\dfrac{1}{x}+\dfrac{2}{x}+\dfrac{3}{x}\right)$$$$=\dfrac{1}{2}$$
$$\therefore\,\,\dfrac{6}{x}=\dfrac{1}{2}$$
$$\therefore\,\,x=12$$
So, $$B$$ takes $$\dfrac{12}{2}=6$$ days to finish the work.
Question 4
1 / -0

How many times are the hands of a clocks coincide in a day?

A
$$10$$

B
$$11$$

C
$$12$$

D
$$22$$

Solution

The hands of the clock makes $$0$$ degrees with each other $$11$$ times in $$12$$ hours.
Therefore, in $$24$$ hours it would coincide $$22$$ times.
Hence, option D is correct.
Question 5
1 / -0

If February 1, 1996 is a Thusrday, then what day is March 10, 1996 ?

A
Monday

B
Sunday

C
Saturday

D
Friday

Solution

$$\displaystyle \because $$ 1996 is a leap year.
$$\displaystyle \therefore $$ Days from 1 Feb to 10 March $$=$$ 39 days $$=$$ 4 odd days.
$$\displaystyle \therefore $$ Thusrday + 3 odd days ($$\displaystyle \because $$ 1 Feb is Thursday) $$=$$ Sunday
Question 6
1 / -0

On what dates of October, 1975 did Tuesday fall ?

A
$$7^{th}, 14^{th}, 21^{st},28^{th}$$

B
$$1^{st}, 8^{th}, 15^{th}, 22^{st},29^{th}$$

C
$$2^{nd}, 9^{th}, 16^{st},23^{rd}, 30^{th}$$

D
$$3^{rd}, 10^{th}, 17^{st}, 24^{th}, 31^{st}$$

Solution

For determining the dates, we find the day on 1st Oct, 1975.
$$1600$$ years have '0' odd days ............(A).
$$300$$ years have '01' odd days ............(B).
$$74$$ years have (18 leap years + 56 ordinary years)
$$2 \times 18 + 1 \times 56 = 92$$ odd days = '01' odd days.....(C)
Days from 1st January to 1st Oct., 1975
1st Jan - 30 June + 1st July to 1st Oct.
$$181 + 31 + 31 + 30 + 1 = 274$$ days $$
$$=\cfrac {274}{7} = '01'$$ odd days................... (D)
Adding (A) + (B) +(C) +(D) $$= 0 + 01 + 01 + 01$$
$$= '03'$$ odd days
Ans. Wednesday( 1st Oct), hence $$7^{th}, 14^{th}, 21^{st},28^{th}$$ Oct. will fall on Tuesday.
Question 7
1 / -0

Robert is travelling on his cycle and has calculated to reach point $$A$$ at $$2$$ $$p.m.$$ If he travels at $$10$$ $$kmph$$, he will reach there at $$12$$ noon, if he travels at $$15$$ $$kmph$$, at what speed must he travel to reach $$A$$ at $$1$$ $$p.m.$$

A
$$8$$ $$kmph$$

B
$$11$$ $$kmph$$

C
$$12$$ $$kmph$$

D
$$14$$ $$kmph$$
Question 8
1 / -0

Find the day of the week on 26 January, 1950.

A
Tuesday

B
Friday

C
Wednesday

D
Thursday

Solution

1600 years have '0' odd days ................ (1)
300 years have 1 odd day..........................(2)
49 years have 12 1eap years and 37 ordinary years.
$$\displaystyle \therefore \quad \left( 12\times 2+37 \right) =\frac { 61 }{ 7 } =5$$odd years...................(3)
26 January has 5 odd days................... (4)
On adding (1), (2), (3) & (4),
11 odd days =04 odd days
$$\displaystyle \therefore $$ day is Thursday.
Question 9
1 / -0

Find the day of the week on 18 July, 1776 (leap year).

A
Monday

B
Tuesday

C
Wednesday

D
Thursday

Solution

Here $$1600$$ years have '0' odd day.................. (A)
$$100$$ years have '5' odd days................. (B).
$$75$$ years = (18 leap years + 57 ordinary years)
$$= (18 \times 2 + 57 \times 1)$$
$$= 93$$ odd days
$$= (7 \times 13 + 2) = 2$$ odd days ....................(C)
Now, the number of days from 1st January to 18 July, 1776
$$= 182 + 18 = 200$$ days
$$= (28 \times 7 + 4)$$ days $$= 4$$ odd days ....................(D)
Adding (A) + (B) +(C) +(D),
We get, $$0 + 5 + 2 + 4 = 4$$ odd days
Hence, the day is Thursday.
Question 10
1 / -0

Find the day of the week on 16 January, 1969

A
Monday

B
Tuesday

C
Wednesday

D
Thursday

Solution

$$1600$$ years have '0' odd day..................... (A)
$$300$$ years have '1' odd day .......................(B)
$$68$$ years have $$17$$ leap years and $$51$$ ordinary years.
Thus $$(17 \times 2 + 51 \times 1)= 85$$ odd days
$$\displaystyle \cong $$ '01' odd day.................... (C)
16 January has $$= 02$$ odd days .........................(D)
Adding (A) + (B) +(C) +(D),
We get, $$0 + 01 + 01 +02 = 04$$ odd days
Ans : Thursday

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Numerical Applications Test 28

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Numerical Applications Test 28

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Question 1

$$50$$ $$\displaystyle m^{3}/min.$$

$$60$$ $$\displaystyle m^{3}/min.$$

$$72$$ $$\displaystyle m^{3}/min.$$

None of these

Solution

Question 2

$$\displaystyle 1\frac{13}{17}$$ hours

$$\displaystyle 2\frac{8}{11}$$ hours

$$\displaystyle 3\frac{9}{17}$$ hours

$$\displaystyle 4\frac{1}{2}$$ hours

Solution

Question 3

$$3$$ days

$$7$$ days

$$4$$ days

$$6$$ days

Solution

Question 4

$$10$$

$$11$$

$$12$$

$$22$$

Solution

Question 5

Monday

Sunday

Saturday

Friday

Solution

Question 6

$$7^{th}, 14^{th}, 21^{st},28^{th}$$

$$1^{st}, 8^{th}, 15^{th}, 22^{st},29^{th}$$

$$2^{nd}, 9^{th}, 16^{st},23^{rd}, 30^{th}$$

$$3^{rd}, 10^{th}, 17^{st}, 24^{th}, 31^{st}$$

Solution

Question 7

$$8$$ $$kmph$$

$$11$$ $$kmph$$

$$12$$ $$kmph$$

$$14$$ $$kmph$$

Question 8

Tuesday

Friday

Wednesday

Thursday

Solution

Question 9

Monday

Tuesday

Wednesday

Thursday

Solution

Question 10

Monday

Tuesday

Wednesday

Thursday

Solution

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