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
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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: 4 weeks ago
A ferry can carry 25 trucks or 40 motorcycles at a time. If there are 15 trucks on the ferry, how many motorcycles can be loaded onto it?
Created: 2 weeks ago
A
18 motorcycles
B
8 motorcycles
C
12 motorcycles
D
16 motorcycles
গণিত
অনুপাত - সমানুপাত (Ration-Proportion-Algebra)
অনুপাত-সমানুপাত (Ratio-Proportion)
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Question: A ferry can carry 25 trucks or 40 motorcycles at a time. If there are 15 trucks on the ferry, how many motorcycles can be loaded onto it?
Solution:
Here,
25 trucks = 40 motorcycles
∴ 1 trucks = 40/25 = 8/5 motorcycles
∴ 15 trucks = = (8 × 15)/5 = 24 motorcycles
∴ Required number of motorcycles = 40 - 24 = 16
So the ferry can carry 16 more motorcycles along with the 15 trucks.
0
Updated: 2 weeks ago
A certain principal amount, invested at simple interest, grows to Tk. 815 after 3 years and Tk. 854 after 4 years. What is the original principal amount?
Created: 4 weeks ago
A
Tk. 658
B
Tk. 612
C
Tk. 698
D
Tk. 710
Solution:
Given,
Amount after 3 years = Tk. 815
Amount after 4 years = Tk. 854
∴ Interest for 1 year = 854 - 815 = Tk. 39
∴ Interest for 3 years = 39 × 3 = Tk. 117
∴ Principal = 815 - 117 = Tk. 698
0
Updated: 4 weeks ago
If 2/3 of X = 75% of Y = 0.4 of Z, then find the ratio X : Y : Z.
Created: 4 weeks ago
A
9 : 8 : 15
B
8 : 10 : 17
C
16 : 7 : 21
D
9 : 13 : 17
Solution:
According to the question,
(2/3) × X = 75% of Y
⇒ 2X/3 = 75Y/100
⇒ 2X/3 = 3Y/4
⇒ X/Y = 9/8
Now,
75% of Y = 0.4 of Z
⇒(75Y/100) = (2Z/5)
⇒ (3Y/4) = (2Z/5)
⇒ 15Y = 8Z
⇒ Y/Z = 8/15
X : Y : Z = (9/8) : 1 : (15/8)
Multiply all terms by 8:
X = 9 × 1 = 9
Y = 1 × 8 = 8
Z = (15/8) × 8 = 15
Therefore,
X : Y : Z = 9 : 8 : 15
0
Updated: 4 weeks ago
