MCQ

MCQ 11 Mark

A tap fills a tank in $8$ hours and another tap at the bottom empties it in $10$ hours. If both work together, the tank will be filled in

A
$18$ hours
B
$24$ hours
C
$36$ hours
✓
$40$ hours

Answer

Correct option: D.

$40$ hours

First tap's $1$ hour work for filling $=\frac{1}{8}$
Second tap's $1$ hour work for emptying $=\frac{1}{10}$
Both work for $1$ hour $=\frac{1}{8}-\frac{1}{10}=\frac{1}{40}$
$\therefore$ The tank will be filled in $40$ hours.

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MCQ 21 Mark

If $5$ pipes can fill the tank in $1$ hour, then $4$ pipes will fill the tank in

✓
$75$ minutes
B
$70$ minutes
C
$65$ minutes
D
none of these

Answer

Correct option: A.

$75$ minutes

$5$ pipes can fill a tank in $1$ hour
Then $4$ pipes will fill in more time
$\therefore \frac{4}{5}=\frac{1}{x} $
$\Rightarrow x=\frac{5}{4}$ hours $=75 $ minutes

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MCQ 31 Mark

A tree $12$ metre high casts a shadow of length $8$ metre. Height of the tree whose shadow is $6$ metre in length is

A
$6 \ m$
✓
$9\ m$
C
$15\ m$
D
none of these

Answer

Correct option: B.

$9\ m$

Shadow of $12\ m$ high tree $=8\ m$
Shadow of another tree $=6\ m$
Let is height $= x\ m$
$\therefore 8: 6:: 12: x$
$\therefore x =\frac{12 \times 6}{8}$
$=\frac{72}{8}$
$=9\ m$

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MCQ 41 Mark

A photograph of bacteria is enlarged $100000$ times attains a length of $5 \ cm,$ then actual length of the bacteria is

A
$0.00005 \ cm$
✓
$5 \times 10^{-5}$
C
$5 \times 10^{-7}$
D
all of these

Answer

Correct option: B.

$5 \times 10^{-5}$

Photograph of bacteria is enlarged $100000$ times attain a length of $5 \ cm$.
$\therefore$ Actual length $=\frac{5}{100000}=5.0 \times 10^{-5}$
$\left(\because 0.00005 \ cm =5.0 \times 10^{-5} \ cm =5 \times 10^{-7} m \right)$

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MCQ 51 Mark

$3$ persons can paint a house in $8$ days, then $4$ persons can paint the same house in

A
$5$ days
✓
$6$ days
C
$7$ days
D
none of these

Answer

Correct option: B.

$6$ days

$3$ persons can paint a house in $8$ days.
$4$ persons will paint it in less days.
$\therefore \frac{4}{3}=\frac{8}{x} \quad $
$\Rightarrow x=\frac{3 \times 8}{4}=6 $ days

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MCQ 61 Mark

In a mess, there was enough food for $200$ students for $20$ days. If $50$ new students joined them, then the food will last for

A
$15$ days
✓
$16$ days
C
$17$ days
D
$18$ days

Answer

Correct option: B.

$16$ days

Food lasts for $200$ students for $=20$ days
Let first will last for $200+50=250$ students $=x$ days
More students, less days
$200: 250:: 20: x$
By inverse variation,
$250: 200:: 20: x$
$x=\frac{200 \times 20}{250}=16$ days

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MCQ 71 Mark

A car travels $80 \ km$ in $5$ litres of petrol, then the distance covered by it in $15$ litres of petrol is

A
$400 \ km$
✓
$240 \ km$
C
$200 \ km$
D
$100 \ km$

Answer

Correct option: B.

$240 \ km$

In $5$ litres, a car travels $=80 \ km$
In $15^{\prime}$ litres, the car will travel $x \ km$
$\therefore 5: 15:: 80: x$
$\Rightarrow x =\frac{15 \times 80}{5}$
$=240$
$\therefore 240 \ km$ distance

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MCQ 81 Mark

If $10-$men can complete a work in $6$ days, then $30$ men can complete the same work in

✓
$2$ days
B
$3$ days
C
$4$ days
D
$5$ days

Answer

Correct option: A.

$2$ days

$10$ men can complete a work in $=6$ days
3$0$ men will complete it in less days $($say $\times$ day$)$
$\therefore \frac{30}{10}=\frac{6}{x} $
$\Rightarrow x=\frac{6 \times 10}{30}=2 $ days

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MCQ 91 Mark

If $5 \ kg$ wheat cost $₹.60$, then cost of $20 \ kg$ wheat is

A
$₹.200$
B
$₹.210$
C
$₹.220$
✓
$₹.240$

Answer

Correct option: D.

$₹.240$

Cost of $5 \ kg$ of wheat $= ₹.60$
Then cost of $20 \ kg$ of wheat
$5 : 20 :: 60 : x ($more wheat, more cost$)$
$\frac{5}{20}=\frac{60}{x}$
$ \Rightarrow x=\frac{20 \times 60}{5} = ₹.240$

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MCQ 101 Mark

If $12$ metre wire costs $₹.24$, then the cost of $8 $ metre wire is

A
$₹.16$
B
$₹.20$
C
$₹.12$
D
$₹.18$

Answer

Cost of $12$ metre wire $= ₹.24$
Cost of $8$ metre wire $= x$
$\therefore 12: 8:: 24: x $
$\Rightarrow x =\frac{8 \times 24}{12}=16$
$\therefore$ Cost of $8$ metre wire $= ₹.16$

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MCQ 111 Mark

Two quantities $x$ and $y$ are said to be in inverse variation if

A
$x y=k$
B
$x \propto \frac{1}{y}$
C
$x =\frac{k}{y}$
✓
all of these

Answer

Correct option: D.

all of these

$x$ and $y$ vary inversely
$\therefore xy =$ constant or $x \propto \frac{1}{y}$
$x =\frac{\text { constant }}{y}$ are correct
All of these.

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