1. The numbers are in the ratio 4:3. If they differ by 18, find these numbers.
2. Three consecutive integers add up to 57. What are these integers?
3. There is a narrow rectangular plot. The length and breadth of the plot are in the ratio of 11:4. At the rate of Rs. 100 per meter it will cost village panchayat Rs. 75000 to fence the plot. What are the dimensions of the plot?
4. Convert the following statements into equations.
(a) 3 added to a number is 11
(b) 2 subtracted from a number is equal to 15.
(c) 3 times a number decreased by 2 is 4.
(d) 2 times the sum of the number x and 7 is 13.
5. Amina thinks of a number and subtracts 5/2 from it. She multiplies the result by 8. The final result is 3 times her original number. Find the number.
6. A number is 12 more than the other. Find the numbers if their sum is 48.
7. The sum of three consecutive odd numbers is 51. Find the numbers.
8. Jane is 6 years older than her younger sister. After 10 years, the sum of their ages will be 50 years. Find their present ages.
9. A sum of Rs.2700 is to be given in the form of 63 prizes. If the prize is of either Rs.100 or Rs.25, find the number of prizes of each type.
10. In an isosceles triangle, the base angles are equal and the vertex angle is 80 degrees. Find the measure of the base angles.
Answers
Answer:
4.
(a)3+x=11
(b)x-2=15
(c)3x-2=4
(d)2*(x+7)
Step-by-step explanation:
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Answer
1. Numbers ratio = 4:3
Let the numbers be, 4x and 3x, where x is the common multiple.
According to the question,
4x - 3x = 18 or 3x - 4x = 18
x = 18 or -18
The numbers are = {4×18, 3×18} or {-4×18, -3×18}
= {72,54} or { -72, -54}
2. Let the three consecutive integers be x-1, x, x+1.
According to the question,
(x-1) + (x) + (x+1) = 54
3x = 54
x = 18
The three integers are 17,18,19.
3. Ratio of length and breadth = 11:4
Let the length, l = 11x, and breadth, b=4x, where x is the common multiple.
Perimeter = 11x + 4x = 15x (m)
According to question, rate = Rs. 100/m.
So, cost = 15x (100) = 75000
1500x = 75000
x = 50
Hence, length = 11x = 11(50) = 550
And, breadth = 4x = 4(50) = 200
4. Let the number be x.
(a) x + 3 = 11
(b) x - 2 = 15
(c) 3x - 2 = 4
(d) 2(x+7) = 13
5. Let the number Amina thinks be x.
On subtracting 5/2 => x - (5/2)
Multiplying by 8 => 8(x - (5/2))
Final result => 3x
So,
8(x - (5/2)) = 3x
8x - 8(5/2) = 3x
8x - 20 = 3x
8x - 3x = 20
5x = 20
x = 4
The number Amina thought was 4.
6. Let one of the number be x.
The other number is 12 more than x, so the other number is (12+x).
The sum of these two numbers is 48, so
x + (12+x) = 48
2x + 12 = 48
2x = 36
x = 18
The numbers are 18, (12+18) => 18, 30
7. Let the three consecutive odd numbers be x-2,x,x+2.
According to the question,
x-2 + x + x+2 = 51
3x = 51
x = 17
The three consecutive numbers are 15,17 and 19.
8. Let the age of younger sister be x.
Age of Jane = x + 6
After ten years their ages will be,
Jane = x + 6 + 10
Sister = x + 10
According to the question,
x + 6 + 10 + x + 10 = 50
2x + 26 = 50
2x = 24
x = 12
Hence, present ages will be,
Jane = x + 6 = 18
Sister = x = 12
9. Given,
Total = Rs. 2700
No. of prizes = 63
Let x be the no. of prizes of Rs. 100.
The remaining prizes are 63-x, of Rs. 25.
So,
100×(x) + 25×(63-x) = 2700
100x + 1575 - 25x = 2700
75x + 1575 = 2700
75x = 1125
x = 15
So, prizes of Rs. 100 are => x = 15
And, prizes of Rs. 25 are => 63-x = 48
10. Given,
Vertex angle = 80°
Let the base angle be x.
As we know, the sum of angles in a triangle is 180°, we get,
80° + x + x = 180°
2x + 80° = 180°
2x = 100°
x = 50°
Hence, the measure of the base angle is x = 50°.