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: 8 hours ago
What is the compound amount of Tk. 3200 for 2 years at a rate of interest 5% per annum?
Created: 8 hours ago
A
Tk. 3500
B
Tk. 3528
C
Tk. 3640
D
Tk. 3568
Question: What is the compound amount of Tk. 3200 for 2
years at a rate of interest 5% per annum?
Solution:
Given,
Principal, P = 3200
Rate, r = 5% = 5/100 = 1/20
Time, n = 2 years
We know,
A = P(1 + r)n
= 3200 × (1 + 1/20)2
= 3200 × (21/20)2
= (3200 × 21 × 21) / (20 × 20)
= (3200 × 441) / 400
= 1411200 / 400
= 3528
∴ The compound amount is Tk. 3528.
0
Updated: 8 hours ago
In how many years will Tk. 750 amount to Tk. 900 at 4% simple interest per annum?
Created: 8 hours ago
A
3.5 years
B
3 years
C
4.5 years
D
5 years
Question: In how many years will Tk. 750 amount to Tk. 900
at 4% simple interest per annum?
Solution:
Simple Interest = Amount - Principal
= 900 - 750
= 150
Here,
Principal, P = 750
Interest Rate, R = 4%
SI = 150
Time, T = ?
SI = PRT/100
⇒ T = (SI × 100)/(P × R)
= (150 × 100)/(750 × 4)
= 15000/3000
= 5 years
0
Updated: 8 hours ago
A bank offers 5% compound interest calculated half-yearly. A customer deposits Tk. 1600 on 1st January and another Tk. 1600 on 1st July of the same year. How much interest will he earn at the end of the year?
Created: 8 hours ago
A
Tk. 129
B
Tk. 121
C
Tk. 118
D
Tk. 132
Question: A bank offers 5% compound interest calculated
half-yearly. A customer deposits Tk. 1600 on 1st January and another Tk. 1600
on 1st July of the same year. How much interest will he earn at the end of the
year?
Solution:
Here,
Half-yearly interest rate = 5% ÷ 2 = (5/2)%
Now,
The first deposit of Tk. 1600 was made on 1st January.
It stays for 12 months, so it earns interest twice, once after 6 months, and
again after 12 months.
So, it earns interest for 2 times (i.e., 2 half-years).
∴ A1 = P(1 + r/100)n
= 1600 × {1 + 5/(2 × 100)}2
= 1600 × {1 + (1/40)}2
= 1600 × (41/40) × (41/40)
= 1600 × 1681/1600
= 1681
Now,
The second deposit of Tk. 1600 was made on 1st July.
It stays for 6 months, so it earns interest only once (1 half-year).
∴ A2 = P(1 + r/100)n
= 1600 × (1 + 1/40)1
= 1600 × (41/40)
= 1640
Total amount = 1681 + 1640 = 3321
Total money deposited = 1600 + 1600 = 3200
∴Interest
earned = 3321 - 3200 = Tk. 121
∴ The customer would have gained Tk. 121 by way of
interest.
0
Updated: 8 hours ago
