The ratio of length and breadth of a rectangular park is 7 : 5. A man runs along its boundary at 8 km/hr and takes 9 minutes for one round. Find its area in sq. meters.
A
82800 sq. m.
B
87500 sq. m.
C
75400 sq. m.
D
90500 sq. m.
উত্তরের বিবরণ
Question: The ratio of length and breadth of a rectangular park is 7 : 5. A man runs along its boundary at 8 km/hr and takes 9 minutes for one round. Find its area in sq. meters.
Solution:
One round of the park is equal to the perimeter of the park.
So, by completing one round, the man covers a distance equal to the perimeter of the park.
Now,
Distance or perimeter = speed × time
= 8 × (9/60)
= 1.2 km
= 1200 meters
Let,
Length = 7x and breadth = 5x
So, Perimeter,
2(7x + 5x) = 1200
⇒ 24x = 1200
∴ x =1200/24 = 50 meters
So, Length = 7 × 50 = 350 meters
And, Breadth = 5 × 50 = 250 meters
Area = Length × Breadth
= 350 × 250
= 87500 sq. m.
0
Updated: 13 hours ago
If 2/3 of X = 75% of Y = 0.4 of Z, then find the ratio X : Y : Z.
Created: 2 months 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: 2 months ago
কোন সংখ্যার ৪০% এর সাথে ৪২ যোগ করলে যোগফল ঐ সংখ্যাটির সমান হবে?
Created: 4 weeks ago
A
৫৬
B
৭০
C
৮৪
D
৯০
গণিত
অনুপাত-সমানুপাত (Ratio-Proportion)
বীজগণিতীয় রাশিমালার যোগ, বিয়োগ, গুণ ও ভাগ (Addition, subtraction, multiplication and division of algebraic expressions)
প্রশ্ন: কোন সংখ্যার ৪০% এর সাথে ৪২ যোগ করলে যোগফল ঐ সংখ্যাটির সমান হবে?
সমাধান:
ধরি, সংখ্যাটি হলো ক
প্রশ্নমতে,
ক এর ৪০% + ৪২ = ক
বা, ক × (৪০/১০০) + ৪২ = ক
বা, ২ক/৫ + ৪২ = ক
বা, (২ক + ২১০)/৫ = ক
বা, ২ক + ২১০ = ৫ক
বা, ৩ক = ২১০
বা, ক = ৭০
সুতরাং, সংখ্যাটি হলো ৭০।
0
Updated: 4 weeks ago
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?
Created: 2 months ago
A
12 : 5
B
12 : 7
C
10 : 7
D
13 : 6
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: 2 months ago
