7%
here. Earned royalties = 1,00,000 TK
Remaining royalties after tax = 1.00.000 – ( 1,00,000 x 20%) = 80,000 TK
Invested at higher rate = 50.000 TK
so, Invested at lower rate = 80.000 – 50,000 = 30,000 TK
Let. Higher rate be = x%
Lower rate be = (x-1)%
According to the question
(50,000× x%× x%×1)+{(30,000 × (x-1)%×1)% ×1)} = 6,100
=> 50,000 $\frac{x}{100} $ + 30,000 $\frac{x-1}{100}$ = 6,100
=> 500x + 300(x -1) = 6,100
=> 500x + 300x -300 = 6,100
=> 800x = 6,100 + 300
so, x = 8
so, Higher rate = 8%
So lower rate = 8 -1 = 7%
32 days
Here. total number of days they worked = 72 days
Let, the wife worked for x days
so, The husband worked for (72 – x) days
According to the question
640x + (72 -x) x 560 = 43,520
=> 640x+ 40,320 -560x = 43,520
=> 80x = 43,520 – 40,320
so, x = 40
So. the wife worked for 40 days days and the husband worked for (72 -40) = 32 days.
Total earnings 66.200 Tk.
Here, the man’s salary in 2015 was = 20,000 Tk.
At 10% increase, the man’s salary in 2016 = 20,000 + 20,000 x 10% = 20,000 + 2,000 = 22.000 Tk.
Similarly, the man’s salary in 2017 was = 22,000 + 22,000 x 10% = 22,000 + 2,200 = 24,200 Tk.
So. he earned in the years 2015 to 2017 inclusive = 20,000 + 22,000 + 24,200 = 66.200 Tk.
See explanation
The sum of the odd numbers from 1 to 125
inclusive = 1 + 3 + 5 + …………+ 125
It’s an arithmetic progression
Where, a= 1; d=3-1 =2
Here. n-th term = 125
so, a+(n-1)d = 125
=> 1+(n-1)2 =125
=> 2n-2 = 125 -1
=> 2n = 124+2
so, n = 63
so, Sum. $s_{n}=\frac{n}{2}[2a+(n-1)d]$
=$\frac{63}{2}[2\times 1+(63-1)\times 2]$
=$\frac{63}{2}$[(2+124)]
= 3969
Again. sum of the odd numbers form 169 to 209 inclusive = 169+171+173+……………………+209
Here. a = 169
d = 171 – 169 = 2
Here, n-th term = 209
so, a+(n-1)d = 209
=> 169+(n-1)2=209
=> 2n-2 = 209-169
=> 2n = 40+2
so, n = 21
Now, Sum $S_{n}=\frac{n}{2}[2a+(n-1)d]$
= $\frac{21}{2}[2\times 169+(21-1)\times 2]$
=3969 [proven]
