1.The ratio of boys and girls in a culb is 3 : 2. Which of the following could be the actual number of members?

(A) 16            (b) 18                 (c) 25             (d) 24

Explanation:  Sum of the ratio = 3 + 2 = 5

\therefore The actual number of members will be divisible by 5. Only option (c) 25 is divisible by 5.

So, correct  answer 25.

2.30% apples out of 450 are rotten. How many apples are in good condition ?

(a) 125                   (b) 315                        (c) 240                  (d)  180

Explanation:

rotten apples=450 \times \frac{{30}}{{100}} = 135

The number of apples in good condition ,

=450 - 450 \times \frac{{30}}{{100}}

= 450 - 135

= 315

3.The present age of son is half of the present age of his mother. Ten years ago, his mother’s age was thrice the age of her son, What is the present age of the son?

(a) 25 years                  (b) 20 years                     (c) 30 years                 (d)  40 years

Exp. Let, age of mother x years

Age of son \frac{x}{2} years

According to question,

x - 10 = \left( {\frac{x}{2} - 10} \right) \times 3

\Rightarrow x - 10 = \left( {\frac{{x - 20}}{2}} \right) \times 3

\Rightarrow 2x - 20 = 3x - 60

\Rightarrow 2x - 3x =  - 60 + 20

\Rightarrow - x = - 40

\therefore x = 40

\therefore Age of son = \frac{{40}}{2} = 20 years

  1. The average to two numbers is 6.5 and square root of their product is 6. What are the numbers?

(a) 11 and 2                  (b) 8 and 5                    (c) 10 and 3               (d)  9 and 4

 

Exp. Let, Two no. be x,y respectively

According to question ,

X + y = 2 \times 6.5

\Rightarrow x + y =13………(i)

And, \sqrt {xy}  = 6

\Rightarrow xy = 36

\Rightarrow x = \frac{{36}}{y}........(ii)

From (i),  \frac{{36}}{y} + y = 13\left[ {\therefore x = \frac{{36}}{y}} \right]

\Rightarrow \frac{{36 + {y^2}}}{y} = 13

\Rightarrow {y^2} - 13y + 36 = 0

\Rightarrow {y^2} - 9y - 4y + 36 = 0

\Rightarrow y(y - 9) - 4(y - 9) = 0

\Rightarrow (y - 9)(y - 4) = 0

\therefore y = 9or,4

\therefore Numbers be 9 and 4.

  1. a is greater than b by 2 and b is greater than c by 10. If a + b + c=130, then (b + c) – a=?

(a) 42                  (b) 38                    (c) 34              (d)  44

Exp. Given, a + b + c = 130

According to question,

a= b + 2

b= c + 10

Again, c = b-10

So, b + 2 + b + b -10=130

\Rightarrow 2b = 130 + 8

\Rightarrow b = \frac{{138}}{3}

\therefore b = 46

a = 46 + 2 = 48

Similarly, c = 46-10=36

\therefore \left( {b + c} \right) - a = \left( {46 + 36} \right) - 48

= 82 - 48 = 34

  1. L. C. M of 5,6,4 and 3 in 60

On dividing 2497 by 60, the remainder is 37

\therefore Number to be added = 60-37=23

7.The face value of 8 in the number 458926 is,

(a) 8000                 (b) 1000                    (c) 8              (d)  8926

Exp. The face value of a digit is the digit itself, at whatever place it may be. It is unchangeable and definite.

So, The face value of 8 in the number 458926 is 8.

8.The total cost of flooring a room at TK 8.50 per square meter is TK 510. If the length of the room is 8 m, its breadth is-

(a) 8.5 m                (b) 7.5 m                   (c) 10.5 m             (d)  12.5 m

Exp. Area of the room = \frac{{510}}{{8.50}} = 60 sq meter

Let, Breadth = x meter

So, 8x = 60

\Rightarrow x = \frac{{60}}{8}

\therefore x = 7.5

9.A can do a piece of work in 4 hours, B and C together in 3 hours, and A and C together in 2 hours. How long will B alone take to do it ?

(a) 8 hours               (b) 12 hours                   (c) 10 hours             (d)  24 hours

Exp. A can do in 1 hour = \frac{1}{4}

(B+C) can do in 1 hour = \frac{1}{3}

\therefore (A+C) can do in 1 hour = \frac{1}{2}

(B-A) can do in 1 hour = \frac{1}{3} - \frac{1}{2}

= \frac{{2 - 3}}{6}

=  - \frac{1}{6}

So, B - A =  - \frac{1}{6}

\Rightarrow B - \frac{1}{4} =  - \frac{1}{6}

\Rightarrow B = \frac{1}{4} - \frac{1}{6}

\Rightarrow B = \frac{{3 - 2}}{{12}}

\therefore B = \frac{1}{{12}}

\therefore Bcan do in 12 hours.

10.A  Speed of 14 meters per second is the same as

(a) 50 km/hr             (b) 46.6 km/hr                   (c) 28 km/hr             (d)  70 km/hr

Exp. 14 meters per second = \left( {14 \times \frac{{18}}{5}} \right) = 50.4km/hr

  1. Oranges are bought at 5 for TK 10 and sold at 6 for TK 15. The gain percent is-

(a) 50%                  (b) 40%                   (c) 25%             (d)  35%

Exp.     Cost price of 1 orange =  TK. \frac{{10}}{5} = 2

Selling price of 1 orange =  TK. \frac{{15}}{6} = 2.5

\therefore Profit percentages = \frac{{2.5 - 2}}{2} \times 100

= \frac{0.5}{2} \times 100 = 25

\therefore 25%

  1. By selling an article for TK. 100, a man gains TK. 15 . Then, his gain % is-

(a) 15%                                                                  (b) 12\frac{2}{3}\%                   (c) 17\frac{1}{4}\%                                    (d)  17\frac{{11}}{{17}}\%

Exp. Cost price  = TK. (100-15) = TK. 85

\therefore Gain % = \frac{{15}}{{85}} \times 100

= \frac{{300}}{{17}}

= 17\frac{{11}}{{17}}

  1. {\left( {0.04} \right)^2} \div \left( {0.008} \right) \times {\left( {0.2} \right)^6} = {\left( {0.2} \right)^?}

(a) 5                  (b) 6                  (c) 8                (d)  None of these

Exp.   {\left( {0.04} \right)^2} \div \left( {0.008} \right) \times {\left( {0.2} \right)^6}

= \frac{{0.0016}}{{0.008}} \times {\left( {0.2} \right)^6}

= 0.2 \times {\left( {0.2} \right)^6}

= {\left( {0.2} \right)^{1 + 6}}

= {\left( {0.2} \right)^7}

  1. Two numbers differ by 5. If their product is 336, then the sum of the two numbers is

(a) 21                  (b) 37                  (c) 28                (d)  51

Exp.   Let, two no be x and y respectively.

So, x – y = 5

xy = 336

\therefore {\left( {x + y} \right)^2} = {\left( {x - y} \right)^2} + 4xy

= {\left( 5 \right)^2} + 4.336

= 25 + 1344

= 1369

\therefore x + y = \sqrt {1369}  = 37

  1. Evaluate : \sqrt {248 + \sqrt {52 + \sqrt {144} } }

(a) 20                  (b) 16                  (c) 24                (d)  30

Exp. \sqrt {248 + \sqrt {52 + \sqrt {144} } }

= \sqrt {248 + \sqrt {52 + 12} }

= \sqrt {248 + \sqrt {64} }

= \sqrt {248 + 8}

= \sqrt {256}

= 16

  1. \left( {0.75 \times 4.4 \times 2.4} \right) \div 0.6 = ?

(a) 4.752                  (b) 12                   (c) 15.84                (d)  13.2

Exp. \left( {0.75 \times 4.4 \times 2.4} \right) \div 0.6 = ?

= \frac{{7.92}}{{0.6}} = 13.2

  1. 48.95 - 32.006 = ?

(a) 4.752                  (b) 12                   (c) 15.84                (d)  13.2

Exp.  48.95 - 32.006

= 16.944

  1. P and Q started a business in the ratio of 2:3. After 1 year P left the business but Q continues. After years they had the profit of TK. 260000. What is the profit of Q ?

(a) TK. 10400            (b) TK. 13000            (c) TK. 15600            (d)  None of these

Exp.  Ratios of Amount ,

P:Q = \left( {2 \times 1} \right):\left( {3 \times 2} \right) = 2:6 = 1:3

So,4x = 26000

\Rightarrow x = 6500

\therefore Profit of Q = 3x = 3 \times 6500 = 19500

  1. How much time will it take for an amount of TK. 450 to yield TK. 81 as interest at 4.5% per annum of simple interest?

(a) 3.5 years                  (b) 4.5 years                   (c) 4 years            (d)  5 years

Exp: we know, Time = \frac{{100 \times \operatorname{int} erest}}{{Rate \times principal}}

= \frac{{100 \times 81}}{{4.5 \times 450}} = 4years

  1. A person crosses a 600 m long street in 5 minuts. What is his speed in km per hour ?

Exp. Speed = \frac{{Dis\tan ce}}{{time}}

= \frac{{600}}{5}m/\sec

= \frac{{\frac{{600}}{{1000}}}}{{\frac{5}{{60}}}}kmh\left[ \begin{gathered}  \because 1km = 1000meter \hfill \\  and1hour = 60\min utes \hfill \\  \end{gathered}  \right]

= \left( {\frac{{600}}{{1000}} \times \frac{{60}}{5}} \right) = 7.2km/h

  1. If 8 man can reap 80 hectares in 24 days, then how many hectares can 36 men reap in 30 days?

(a) 350                 (b) 400                  (c) 450             (d)  425

Exp. Let, x hectares be required

According to question,

\frac{x}{{36 \times 30}} = \frac{{80}}{{8 \times 24}}

\Rightarrow x = \frac{{80 \times 36 \times 30}}{{8 \times 24}}

\Rightarrow x = \frac{{86400}}{{192}}

\therefore x = 450

  1. The ratio 5:4 expressed as a percent equals

(a) 125%                  (b) 40%                   (c) 80%             (d)  12%

Exp. \frac{5}{4} \times 100 = 125\%

  1. The average of 6 numbers is 7. The average of three numbers of them is 5. What will be average of the remaining numbers ?

(a)  15                (b)  30                  (c) 42            (d)  9

Exp.  Average of remaining three no.

= \frac{{6 \times 7 - 3 \times 5}}{3}

= \frac{{42 - 15}}{3}

= \frac{{27}}{3}

= 9

  1. In a group of 52 persons, 16 drink tea but not coffee 33 drink tea. How many drink coffee but not tea?

(a)  3                (b)  7                   (c) 19            (d)  17

Exp.   Tea = 16

Both = 17

\left[ {\therefore 33 - 16 = 17} \right]

Coffee = 19

\left[ {\therefore 52 - 33 = 19} \right]

\therefore Ans : 19

  1. The last prime number is

(a)  0               (b)  1                   (c) 3            (d)  2

Ans:   (d)  2

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