Exercise 9.1
1. If x: y = 3: 5, find the ratio 3x + 4y: 8x + 5y.a
Solution:
We have,
2. If x: y = 8: 9, find the ratio (7x – 4y): 3x + 2y.
Solution:
3. If two numbers are in the ratio 6:13 and their L.C.M is 312, find the numbers.
Solution:
Let the required numbers be 6x and 13x
Than their L.CM is 78x
78x = 312
X = 312/78
= 4
Thus,
The numbers are
6x = 6×4 = 24
13x = 13×4 = 52
4. Two numbers are in the ratio 3: 5. If 8 is added to each number, the ratio becomes 2: 3. Find the numbers
Solution:
Let the required numbers be 3x and 5x
Given that if is added ti each other than ratio becomes 2 : 3
That is 3x + 8 : 5x + 8 = 2 : 3
(3x + 8)/ (5x + 8) = 2/3
3 (3x+8) = 2 (5x + 8)
9x + 24 = 10x + 16
By transposing
24 – 16 = 10x – 9x
X = 8
Thus the numbers are 3x = (8) = 24
And 5x = 5 (8) = 40
5. What should be added to each term of the ratio 7: 13 so that the ratio becomes 2: 3
Solution:
Let the number to be added be x
Then
(7+x)3 = 2 (13+x)
3x – 2x = 26- 21
= x = 5
Then,the required number is 5
6. Three numbers are in the ratio 2: 3: 5 and the sum of these numbers is 800. Find the numbers
Solution:
According to question,
Three numbers are in ratio 2: 3: 5
Sum of these numbers = 8000
Sum o the terns of the ratio 2+ 3+5 = 10
7. The ages of two persons are in the ratio 5: 7. Eighteen years ago their ages were in the ratio 8: 13. Find their present ages.
Solution:
Let the required be 5x and 7x
18 years ago their age ratios
65x – 1318 = 87x – 8 18
65x- 234 = 56x – 144
65x – 56x = 234 – 144
9x = 90
X = 10
Thus the ages are 5x = 510 = 50 years
7x=710 = 70 years
8. Two numbers are in the ratio 7: 11. If 7 is added to each of the numbers, the ratio becomes 2: 3. Find the numbers.
Solution:
Let the required numbers be 7x and 11x
If 7 is added to each of the numbers
It becomes
= 21x + 21 = 22x + 14
= x = 21 – 14 = 7
Thus, the numbers are 7x = 7×7 = 49
11x = 11×7 = 77.
9. Two numbers are in the ratio 2: 7. 11 the sum of the numbers is 810. Find the numbers.
Solution:
Given that numbers in the ratio 2:7
And their sum = 810
Sum of terms in the ratio 2 + 7= 9
= 2 ×90
= 180
Second number = (7/9)×810
= 7×90
= 630
10. Divide Rs 1350 between Ravish and Shikha in the ratio 2: 3.
Solution:
We have,
Sum of the terms of the ratio = 2 + 3= 5
11. Divide Rs 2000 among P, Q, R in the ratio 2: 3: 5.
Solution:
Given total amount to be divided = 2000
Sum of the terms of the ratio = 2+ 3 + 5 = 10
P’s share of money = (2/10)×2000
= 2×200
= Rs. 400
And Q’s share of money = (3/10) ×2000
= 3 × 200
= Rs. 600
And R’s share of money = (5/10) ×2000
= 5×200
= Rs. 1000
12. The boys and the girls in a school are in the ratio 7:4. If total strength of the school be 550, find the number of boys and girls.
Solution:
We have,
The boys and girl is in the ratio 7:4
Sum of the terms in the ratio = 7+4=11
Total strength = 550
= 4×50
= 200 girls
13. The ratio of monthly income to the savings of a family is 7: 2. If the savings be of Rs. 500, find the income and expenditure.
Solution:
According to question,
The ratio of income and savings is 7: 2
Savings
2x = 500
So, x = 250
Therefore,
Income = 7 × 250 = 1750
Expenditure = Income – savings
= 1750 – 500
= Rs.1250
14. The sides of a triangle are in the ratio 1: 2: 3. If the perimeter is 36 cm, find its sides.
Solution:
The sides of a triangle are in the ratio
1:2:3
Sum of the terms in the ratio = 1+ 2+ 3 = 6
Perimiter = 36 cm
15. A sum of Rs 5500 is to be divided between Raman and Amen in the rate 2: 3. How much will each get?
Solution:
16. The ratio of zinc and copper in an alloy is 7: 9. It the weight of the copper in the alloy is 11.7 kg, find the weight of the zinc in the alloy.
Solution:
The ratio of zinc and copper un an alloy = 7:9
Weight of copper in the alloy = 11.7kg
9x = 11.7 kg
X = 11.7/9
Weight of zinc in the alloy = 11×7
= 9.10kg
Then, weight of zinc = 9.10 kg
17. In the ratio 7: 8. If the consequent is 40, what a the antecedent
Solution:
Given ratio = 7: 8
Consequent
8x = 40
x = 40/8
x = 5
18. Divide Rs 351 into two parts such that one may be to the other as 2: 7
Solution:
Given total amount is to be divided = 351
Ratio 2:7
The sum of terms = 2+ 7
= 9
First ratio of amount= (2/9)×351
= 7×39
= Rs. 273
19. Find the ratio of the price of pencil to that of ball pen, if pencil cost Rs.16 per score and ball pen cost Rs.8.40 per dozen.
Solution:
20. In a class, one out of every six students fails. If there are 42 students in the class, how many pass?
Solution:
Given,
One out of 6 student fails
x out of 42 students
16 = x/42
x = 42/6
x = 7
Number of students who fail = 7 students
No of students who pass =Total students – Number of students who fail = 42 – 7 = 35 students.