Question 1:
383285.24 sq. mile
We know, 1 km = 0.62 mile
1 sq. km = 0.62 x 0.62 = 0.3844 sq. mile
997100 sq. km = 997100 x 0.3844
= 383285.24 sq. mile
85000 TK
Let, Mr. Rahman invested Tk. x at 7 5% profit.
For Tk. 100 Rahman gets Tk. 7.5
For Tk. x Rahman gets Tk. $\frac{7.5x}{100}$
Mr Rahman invested Tk. (190000 —x) at 6%
For Tk. 100 Rahman gets Tk. 6
For Tk. (190000 —x) Rahman gets Tk. $\frac{6(190000)}{100}$
Here we can say,
$\frac{7.5x}{100} + \frac{6(190000)}{100}$= 12675
=> 1.5x = 1267500 — 1140000
=> 1.5x = 127500
So, x = 85000 Tk.
15 km
Let, the distance between A and B is x km
The man travels between A and B 3 km in 1 hour
The man travels between A and B x km in $\frac{x}{3}$ hour
The man returns from B to A at the rate of 5 km. per hour
He takes time $\frac{x}{5}$ hour for return
According to question,-
$\frac{x}{3} + \frac{x}{5}$ = 8
=> x = $\frac{8\cdot15}{8}$
x = 15km
12.36 %
Length and with of the rectangular field is 24 metre and 12 metre respectively
Area of the rectangular 24 x 12 sq. metre = 288 sq. metre
Both length and width increased by 6%
Increased length = 24 + 6% of 24
= $\frac{24 +1.44}{100}$
= 25.44 metre
Increased width = 12 + 6% of 12
= 12 + 0.72 = 12.72 metre
Total area after increased = (25.44 x 12.72) sq. metre
= 323.5968 sq. metre
So, Increased percentage = $\frac{(323.5968-288)\cdot100)}{288}$ = 12.36 %
Question 5:
Profit rate is 25%
Suppose, buying price of of 5 mangoes Tk. 1
Price of 5 mangoes in Tk. 1
Price of 1 mangoe in Tk $\frac{1}{5}$
Again, selling price of 4 mangoes is Tk. 1
selling price of 1 mangoes is $\frac{1}{4}$
Profit = $\frac{1}{4} – \frac{1}{5}$
= $\frac{1}{20}$
Tk. $\frac{1}{5}$ makes profit = Tk. 20
Tk. 100 makes profit = Tk. $\frac{1\cdot4\cdot100}{20\cdot1}$
= Tk. 25
So, Profit rate is 25%
