The ratio of the present ages of a mother and son is 7 : 2. After 7 years, the ratio of their ages becomes 8 : 3. What will be the ratio of their ages after 11 years?
A
12 : 5
B
12 : 7
C
10 : 7
D
13 : 6
উত্তরের বিবরণ
Question: The ratio of the present ages of a mother and son
is 7 : 2. After 7 years, the ratio of their ages becomes 8 : 3. What will be
the ratio of their ages after 11 years?
Solution:
Let,
The present age of the mother = 7x years
The present age of the son = 2x years
After 7 years, their ages will be:
Mother = (7x + 7) years
Son = (2x + 7) years
According to the question,
(7x + 7)/(2x + 7) = 8/3
⇒
3(7x + 7) = 8(2x + 7)
⇒
21x + 21 = 16x + 56
⇒
21x - 16x = 56 - 21
⇒
5x = 35
⇒
x = 35/5
∴
x = 7
Present age of mother = 7 × 7 = 49 years
Present age of son = 2 × 7 = 14 years
Now, after 11 years,
Mother's age = 49 + 11 = 60 years
Son's age = 14 + 11 = 25 years
∴ The ratio of their ages after 11 years,
= 60 : 25
= 12 : 5
0
Updated: 1 month ago
At what rate of compound interest per annum will a sum of Tk. 1600 becomes Tk. 2304 in 2 years?
Created: 1 month ago
A
20%
B
15%
C
12%
D
30%
Question: At what rate of compound interest per annum will a
sum of Tk. 1600 becomes Tk. 2304 in 2 years?
Solution:
Principal, P = 1600 টাকা
Amount, A = 2304 টাকা
Time, n = 2 years
Rate, r = ?
We know,
A = P × (1 + r/100)n
⇒
2304 = 1600 × (1 + r/100)2
⇒
(1 + r/100)2 = 2304/1600
⇒
(1 + r/100) = 48/40 [উভয়পাশে
বর্গমূল করে]
⇒
1 + r/100 = 6/5
⇒
r/100 = 6/5 - 1
⇒
r/100 = (6 - 5)/5
⇒
r/100 = 1/5
⇒
r = 100/5
∴
r = 20
∴ Interest rate 20%
0
Updated: 1 month ago
Tk. 1,000 becomes Tk. 1,200 in 4 years at a certain rate of simple interest. If the rate of interest is increased by 2%, what amount will Tk. 1,000 become in 4 years?
Created: 1 month ago
A
Tk. 1240
B
Tk. 1280
C
Tk. 1300
D
Tk. 1340
Question: Tk. 1,000 becomes Tk. 1,200 in 4 years at a
certain rate of simple interest. If the rate of interest is increased by 2%,
what amount will Tk. 1,000 become in 4 years?
Solution:
Principal, P = 1000
Interest, I = 1,200 - 1,000 = 200
Time, T = 4 years
SI = PRT/100
⇒
R = (SI × 100)/(P × n)
⇒
R = (200 × 100)/(1000 × 4)
⇒
R = 20000/4000
⇒ R = 5
∴ Interest rate, R = 5%
∴ New Interest rate = 5% + 2% = 7%
New interest at 7% for 4 years:
New interest = (1,000 × 7 × 4)/100
= (28,000)/100
= 280 Tk.
New amount = Principal + Interest
= 1,000 + 280
= Tk. 1,280
0
Updated: 1 month ago
How many years will Tk. 1500 need at 4% simple interest to earn the same interest as Tk. 2000 earns in 3 years at 5% simple interest?
Created: 1 month ago
A
4 years
B
5 years
C
6 years
D
8 years
Question: How many years will Tk. 1500 need at 4% simple
interest to earn the same interest as Tk. 2000 earns in 3 years at 5% simple
interest?
Solution:
Interest from Tk. 2000 in 3 years at 5%:
SI = (P × R × T)/100
= (2000 × 5 × 3)/100
= 300 Tk.
Now,
Tk. 1500 to Produce the Same Interest (Tk. 300) at 4%:
Principal, P = Tk. 1500
Interest, SI = Tk. 300
Interest Rate, R = 4%
Time, T = ? years
SI = PRT/100
⇒
T = (SI × 100)/(P × R)
⇒
T = (300 × 100)/(1500 × 4)
⇒
T = 30000/6000
∴
T = 5 years
0
Updated: 1 month ago
