X,y and z share an amount in the ratio 1:2:3 if z recive 28 more then x then what is the total amount
Answers
Answered by
0
Four numbers are in a proportion if the product of extremes = product of means.
E.g. if a : b :: c : d, then ad = bc
If the ratio of first and second equals to the ratio of second and third (with three or more quantities), they are said to be in continued proportion.
E.g. if a/b = b/c, then a, b and c are in a continued proportion.
If a number, say Z, is divided into three parts, whose ratio is a:b:c, then:
First part =
Second part =
Third part =
Illustration 1: The ratio of number of ladies to gents in a party was 1:2, but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were originally present at the party?
4
8
12
16
Solution:Let the number of ladies be x& the number of gents be 2x
3x-6 =2x -2
Total number of persons at the party = 3x =3 × 4 = 12
Illustration 2: The sum of the present ages of A, B and C is 30 years. Six year ago, their ages were in the ratio 1: 2: 3. What is the present age of C?
36
42
50
24
Solution: Sum of the ages of A, B, C six years ago = 90 – 3
= 72 years
Now,
Six years ago, the ages of A, B & C were in ratio 1:2:3
Age of C six years ago =
= 36 years
Present age of C = 36 +6
= 42 years
Illustration 3: If bc : ac: ab = 1:2:3, find :
1 :3
9 :1
4 :9
4 :1
Solution: : / =
Also bc : ac = 1:2
=
: = = 2 =
Illustration 4: The sum of the squares of three numbers is 532 and the ratio of the first to the second as also of the second to the third is 3:2. What is the second number?
12
18
15
21
Solution: = , =
A =B & C = B
Now,
A2 + B2 + C2 = 532
B2 + B2 + = 532
= 532
133B2 = 532 × 36
B =12
Illustration 5: A person distributes his pens among four friends A, B, C and D in the ratio 1/3: 1/4: 1/5: 1/6. What is the minimum number of pens that the person should have to perform this exercise?
60
57
48
52
Solution: LCM of 3, 4, 5, 6 = 60
So, the pens are distributed among A, B, C & D in the ratio
15 : 12 : 10
Total number of pens = 20x + 15x + 12x + 10x
To gauge the minimum number of pens, the value of x should be taken as 1
=20 + 15 + 12 + 10 = 57
E.g. if a : b :: c : d, then ad = bc
If the ratio of first and second equals to the ratio of second and third (with three or more quantities), they are said to be in continued proportion.
E.g. if a/b = b/c, then a, b and c are in a continued proportion.
If a number, say Z, is divided into three parts, whose ratio is a:b:c, then:
First part =
Second part =
Third part =
Illustration 1: The ratio of number of ladies to gents in a party was 1:2, but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were originally present at the party?
4
8
12
16
Solution:Let the number of ladies be x& the number of gents be 2x
3x-6 =2x -2
Total number of persons at the party = 3x =3 × 4 = 12
Illustration 2: The sum of the present ages of A, B and C is 30 years. Six year ago, their ages were in the ratio 1: 2: 3. What is the present age of C?
36
42
50
24
Solution: Sum of the ages of A, B, C six years ago = 90 – 3
= 72 years
Now,
Six years ago, the ages of A, B & C were in ratio 1:2:3
Age of C six years ago =
= 36 years
Present age of C = 36 +6
= 42 years
Illustration 3: If bc : ac: ab = 1:2:3, find :
1 :3
9 :1
4 :9
4 :1
Solution: : / =
Also bc : ac = 1:2
=
: = = 2 =
Illustration 4: The sum of the squares of three numbers is 532 and the ratio of the first to the second as also of the second to the third is 3:2. What is the second number?
12
18
15
21
Solution: = , =
A =B & C = B
Now,
A2 + B2 + C2 = 532
B2 + B2 + = 532
= 532
133B2 = 532 × 36
B =12
Illustration 5: A person distributes his pens among four friends A, B, C and D in the ratio 1/3: 1/4: 1/5: 1/6. What is the minimum number of pens that the person should have to perform this exercise?
60
57
48
52
Solution: LCM of 3, 4, 5, 6 = 60
So, the pens are distributed among A, B, C & D in the ratio
15 : 12 : 10
Total number of pens = 20x + 15x + 12x + 10x
To gauge the minimum number of pens, the value of x should be taken as 1
=20 + 15 + 12 + 10 = 57
Answered by
0
Concept:
The ratio of two numbers shows how many times the first number contains the second number.
Given:
x, y, and z share an amount in 1:2:3, and z receives 28 more than the x.
Find:
The total amount that is shared.
Solution:
As the ratio of the amount distributed to x, y and z are 1: 2 : 3.
Let the amount distributed to x be a. So, the amount distributed to y and z is 2a and 3a respectively.
Also, given that, z = x + 28
and, x = a, y = 2a and z = 3a.
Substituting and equating the values,
3a = a + 28
2a = 28
a = 28/2
a = 14
The total amount is a + 2a + 3a as the amount is distributed to x, y, and z.
Total amount = a + 2a + 3a = 6a
Total amount = 6 × 14 = 84
Hence, the total amount that is shared by x, y, and z is 84.
#SPJ2
Similar questions