Pubali Bank Ltd - Junior Officer/Junior Officer(Cash) - 18.07.2014/গণিত এর প্রশ্ন পরুন ।

প্রশ্নঃ In a city , 40% of the people are illiterate and 60% are poor. Among the rich , 10% are illiterate. What percentage of the poor population is illiterate?

বর্ণনাঃ

Let, total = 100 people, then, poor = 60, rich = 40.
illiterate rich = 10% of 40 = 4
poor = 40 - 4 = 36
Let, x% is illeterate poor
x% of 60 = 36
$\Rightarrow \frac{x}{100}\times 60=36$
$\therefore x=1000$

প্রশ্নঃ A number is decreased by 10% and then increased by 10% . The number so obtained is 10 less than the original number. what was the original number ?

বর্ণনাঃ

Let the number x. After decrease by 10%, the number is .90x then it is increase by 10%
and becomes .90x $\times$ 1.1 = .90x
Now, x $-$ .99x = 10
$\Rightarrow$ x  = 1000

প্রশ্নঃ In a fraction , if numerator is increased by 40% and denominator is increased by 80% then what fraction of the original is the new fraction ?

বর্ণনাঃ

Let the fraction be $\frac{y}{x}$ .
After the changes, it becomes $\frac{1.4y}{1.8x} =\frac{7y}{9x}=\frac{7}{9}$ of $\frac{y}{x}$

প্রশ্নঃ In an examination , 34% of the students failed in Mathematics and 42% failed in English . If 20% of the students failed in both the subjects , then the percentage of students who passed in both the subjects was:

বর্ণনাঃ

% passed in both = 100 $-\left\{34+42-20\right\}$ = 44

প্রশ্নঃ A sum invested at 5% simple interest per annum grows to Tk. 504 in 4 years The same amount at 10% simple interest per annum in $2\frac{1}{2}$ years will grow to :

বর্ণনাঃ

$$\begin{gathered} \frac{F_2}{F_1}=\frac{p(1+n_2{r}_2)}{p(1+n_1{r}_1)} \\ =\frac{1+2.5\times .10}{1+4\times .05}=\frac{1.25}{1.2} \\ \therefore F_2=\frac{1.25}{1.2}\times F1 \\ =\frac{1.25}{1.2}\times 504 \\ =500 \end{gathered}$$

প্রশ্নঃ A person borrows Tk. 5000 for 2 years at 4% p.a. simple interest . He immediately lends to another person at $6\frac{1}{4}\%p.a.for2years.Findhisgaininthetransactionperyear.$

বর্ণনাঃ

Gain in 2 years
$=\left(5000\times \frac{25}{4}\times \frac{2}{100}\right)-\left(\frac{5000\times 4\times 2}{100}\right)=625-400-225$
$\therefore$ Gain in 1 years =(225$÷$2) = 112.50 Tk.

প্রশ্নঃ A contractor employed 30 men to do a piece of work in 38 days. After 25 days , he employed 5 men more and the work was finished one day earlier. How many days he would have been behind, if he had not employed additional men?

বর্ণনাঃ

remaining no of days = 38 -25 = 13, the work was finished 1 day earlier.
So 35 men can complete the work in 12 days
$\therefore$ 1 ,, ,, ,, ,, $12\times 35$
$\therefore$ 30 ,, ,, ,, ,, $\frac{{\displaystyle 12\times 35}}{30}$ ,,
= 14 days
The contractor would bd (14 - 13) Or, 1 day behind.

প্রশ্নঃ A garrison of 500 men had provisions for 27 days . After 3 days a reinforcement of 300 men arrived . For how many more days will the remaining food last now?

বর্ণনাঃ

500 men had provisions for (27 - 3) = 24 days
$\therefore$ 1 ,, ,, ,, ,, $500\times 24$
$\therefore$ (500+300) Or, 800 ,, ,, $\frac{{\displaystyle 500\times 24}}{800}$
= 15 days

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

বর্ণনাঃ

8 men in 24 days reap 80 hectares
$\therefore$ 1 ,,  ,,      1 ,,   ,, $\frac{{\displaystyle 80}}{8\times 24}$ ,,
$\therefore$ 36 ,, ,, 30 ,, ,,  $\frac{{\displaystyle 80\times 36\times 30}}{8\times 24}$
Or, 450 hectares

প্রশ্নঃ A man completes $\frac{4}{5}ofajobin10days.Atthisrate,howmanymoredayswillittakehimtofinishthejob?$

বর্ণনাঃ

He completes $\frac{5}{8}$ of a job in 10 days
$\therefore$ ,,   1 ,, ,, ,, $\frac{10\times 8}{5}$  ,,
=16 days
So (16 - 10 )Or 6 more days are required.

প্রশ্নঃ If the radius of a circle is increased by 6% , then the area is increased by :

বর্ণনাঃ

Let original radius r, after 6% increase it is 1.06 r
$\frac{A_2}{A_1}=\frac{\mathrm{\pi }(1.06\mathrm{r}{)}^2}{{\mathrm{\pi r}}^2}$
= 1.1236 = 1.1236 $\times$ 100%
= 112.36%
So increase = (112.36 - 100)% = 12.36%

প্রশ্নঃ If the height of a triangle is decreased by 40% and its base is increased by 40% , what will be the effect on its area?

বর্ণনাঃ

$\frac{{\displaystyle Are{a}_2}}{Are{a}_1}= \frac{{\displaystyle \frac{1}{2}\times .60A\times 1.4B}}{{\displaystyle \frac{1}{2}\times A\times B}}=.84$
$Are{a}_2$ = .84 of $Are{a}_1$ .
=(1. - .16) of $Are{a}_1$.
$\therefore$ 16% decrease.

প্রশ্নঃ A tank is 25 m long , 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq.m is :

বর্ণনাঃ

Area to be plastered = $\left[2(l+b)\times h\right] + (l\times b)$
= $\left[2(\mathit{25}+12)\times 6\right] + (25\times 12)$
= (444 + 300)
= 744$m^2$
$\therefore$ Cost of plastering = $\left(744\times \frac{75}{100}\right)$ Tk.
= 558Tk.

প্রশ্নঃ The diagonal of a square is $4\sqrt{2}$ cm. The diagonal of another square whose area is double that of the first square , is:

বর্ণনাঃ

diagonal = $a\sqrt{2}=4\sqrt{2}$
$\therefore$ side = a = 4
$\therefore$  area = 4$\times$ 4= 16
$\therefore$ 2 $\times$ area = 16 $\times$ 2 = 32
New area = 32
New side = $\sqrt{32}=\sqrt{4\times 8}=2\sqrt{8}$
New diagonal = $2\sqrt{8}\times \sqrt{2}=2\sqrt{8\times 2}=2\sqrt{16}=2\times 4$ = 8cm 

প্রশ্নঃ 10% loss on selling price is what percent loss on the cost price ?

বর্ণনাঃ

loss on cost rice is same as loss on selling price. It is usually just referred to as ''loss''.

প্রশ্নঃ The cost price of 20 articles is the same as the selling price of x articles . If the profit is 25% , then the value of x is :

বর্ণনাঃ

Let C.P of each article be   1.
,,    ,,   x  ,,  is x
S.P ,, ,, x ,, is  20
Profit = (20 - x)
$\therefore \frac{20-x}{x}\times 100=25$
$\Rightarrow$ 2000 - 100x = 25x
$\Rightarrow$ 125x = 2000
$\therefore$ x = 16

প্রশ্নঃ At what profit percent must an article be sold so that by selling at half that price , there may be a loss of 30% ?

বর্ণনাঃ

Let Cost Price, C.P = 100
at x% profit, selling price = 100 + x
at 30% loss, s.p = 70
Now, $\frac{100+x}{2}$  = 70 
$\Rightarrow$ 100 + x = 140
$\Rightarrow$ x = 40

প্রশ্নঃ The sale price of an article including the sales tax is TK. 616 . The rate of sales tax 10% If the shopkeeper has made a profit of 12% , then the cost price of the article is :

বর্ণনাঃ

Let the C.P. of the article be x Tk.
The s.p.= $x\times 1.12\times 1.1$ 
Given $x\times 1.12\times 1.1$ = 616
$\Rightarrow$ x = $\frac{616}{1.232}$ = 500

প্রশ্নঃ An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours . To cover the same distance in $1\frac{2}{3}hours,itmusttravelataspeedof:$

বর্ণনাঃ

Distance = ($240\times 5$) = 1200km
$\Rightarrow$ Speed = 1200/(5/3)  km/hr
$\therefore$ Required speed = ($1200\times \frac{3}{5}$) = 720 km/hr

প্রশ্নঃ A clock is started at noon . By 10 minutes past 5, the hour hand has turned through:

বর্ণনাঃ

Angle traced by hour hand in 12 hrs = 360$°$
,, ,, ,, ,, ,, in 5 hrs 10 min i.e. $\frac{31}{6}$  hrs
=($\frac{360}{12}\times \frac{31}{6}$) = 155$°$