Ratio, Proportion
- Two numbers are in the ratio 5 : 7. On diminishing each of them by 40, they become in the ratio 17 : 27. The difference of the numbers is :
-
View Hint View Answer Discuss in Forum
Let the two numbers are x and y.
According to the question,x = 5 y 7
7x = 5y
7x – 5y = 0 ...(I)Again, x − 40 = 17 y − 40 27
⇒ 27x – 1080 = 17y – 680
⇒ 27x – 17y = 1080 – 680
⇒ 27x – 17y = 400 ...(II)
From (I) × 17 – (II) × 5, we have
Putting the value of x in equation (I)
7 × 125 = 5y∴ y = 7 × 125 = 175 5
∴ Difference of the numbers
= 175 – 125 = 50
Second Method :
Here, a = 5, b = 7, x = 40
c = 17, d = 27
The two numbers are= xa(d − c) ad − bc = 40 × 5(27 − 17) 5 × 27 − 7 × 17 = 200 × 10 135 − 119 = 2000 = 500 16 4
1st Number = 125And = xb(d − c) ad − bc = 40 × 7(27 − 17) 5 × 27 − 7 × 17 = 280 × 10 135 − 119 = 2800 = 700 16 4
2nd Number = 175
Their difference= 175 – 125 = 50Correct Option: D
Let the two numbers are x and y.
According to the question,x = 5 y 7
7x = 5y
7x – 5y = 0 ...(I)Again, x − 40 = 17 y − 40 27
⇒ 27x – 1080 = 17y – 680
⇒ 27x – 17y = 1080 – 680
⇒ 27x – 17y = 400 ...(II)
From (I) × 17 – (II) × 5, we have
Putting the value of x in equation (I)
7 × 125 = 5y∴ y = 7 × 125 = 175 5
∴ Difference of the numbers
= 175 – 125 = 50
Second Method :
Here, a = 5, b = 7, x = 40
c = 17, d = 27
The two numbers are= xa(d − c) ad − bc = 40 × 5(27 − 17) 5 × 27 − 7 × 17 = 200 × 10 135 − 119 = 2000 = 500 16 4
1st Number = 125And = xb(d − c) ad − bc = 40 × 7(27 − 17) 5 × 27 − 7 × 17 = 280 × 10 135 − 119 = 2800 = 700 16 4
2nd Number = 175
Their difference= 175 – 125 = 50
- The ratio between two numbers is 3 : 4. If each number is increased by 6, the ratio becomes 4 : 5. The difference between the numbers is
-
View Hint View Answer Discuss in Forum
Let the numbers be 3x and 4x.
∴ 3x + 6 = 4 4x + 6 5
⇒ 16x + 24 = 15x + 30
⇒ x = 30 – 24 = 6
∴ Required difference = 6
Second Method :
Here, a = 3, b= 4, x = 6
c = 4, d = 5The numbers are = xa(c − d) ad − bc = 6.3(4 − 5) 3 × 5 − 4 × 4 = 18 × −1 = 18 15 − 16 = xb(c − d) ad − bc = 6 × 4(4 − 5) 3 × 5 − 4 × 4 = 24 × (− 1) = 24 15 − 16
Numbers are 24 and 18.
Their difference = 24 – 18 = 6Correct Option: C
Let the numbers be 3x and 4x.
∴ 3x + 6 = 4 4x + 6 5
⇒ 16x + 24 = 15x + 30
⇒ x = 30 – 24 = 6
∴ Required difference = 6
Second Method :
Here, a = 3, b= 4, x = 6
c = 4, d = 5The numbers are = xa(c − d) ad − bc = 6.3(4 − 5) 3 × 5 − 4 × 4 = 18 × −1 = 18 15 − 16 = xb(c − d) ad − bc = 6 × 4(4 − 5) 3 × 5 − 4 × 4 = 24 × (− 1) = 24 15 − 16
Numbers are 24 and 18.
Their difference = 24 – 18 = 6
- The two numbers are in the ratio 2 : 3 and their product is 96. The sum of the numbers is
-
View Hint View Answer Discuss in Forum
Let the numbers be 2x and 3x.
∴ 2x × 3x = 96⇒ x2 = 96 = 16 6
∴ x = √16 = 4
∴ Sum = 2x + 3x = 5x
= 5 × 4 = 20Correct Option: B
Let the numbers be 2x and 3x.
∴ 2x × 3x = 96⇒ x2 = 96 = 16 6
∴ x = √16 = 4
∴ Sum = 2x + 3x = 5x
= 5 × 4 = 20
- When a particular number is subtracted from each of 7, 9, 11 and 15, the resulting numbers are in proportion. The number to be subtracted is :
-
View Hint View Answer Discuss in Forum
Let the number to be subtracted be x.
According to the question,7 − x = 11 − x 9 − x 15 − x
Now, check through options
Clearly, putting x = 3,Each ratio = 2 . 3
Note : Solve such questions orally by mental exercise.
Second Method :
The number will be x= ad − bc (a + d) − (a − d) = 7 × 15 − 9 × 11 (7 + 15) − (9 + 11) = 105 − 99 22 − 20 = 6 = 3 2 Correct Option: C
Let the number to be subtracted be x.
According to the question,7 − x = 11 − x 9 − x 15 − x
Now, check through options
Clearly, putting x = 3,Each ratio = 2 . 3
Note : Solve such questions orally by mental exercise.
Second Method :
The number will be x= ad − bc (a + d) − (a − d) = 7 × 15 − 9 × 11 (7 + 15) − (9 + 11) = 105 − 99 22 − 20 = 6 = 3 2
- The sum of three numbers is 68. If the ratio of the first to the second be 2 : 3 and that of the second to the third be 5 : 3, then the second number is
-
View Hint View Answer Discuss in Forum
Let the numbers be a, b and
c. Then
a : b = 2 : 3
b : c = 5 : 3
∴ a : b : c = 2×5 : 3×5 : 3×3
= 10 : 15 : 9
Let the numbers now be 10x, 15x and 9x
∴ 10 x + 15x + 9x = 68⇒ 34x = 68 ⇒ x = 68 = 2 34
∴ Second number = 15 x
= 15 × 2 = 30Correct Option: A
Let the numbers be a, b and
c. Then
a : b = 2 : 3
b : c = 5 : 3
∴ a : b : c = 2×5 : 3×5 : 3×3
= 10 : 15 : 9
Let the numbers now be 10x, 15x and 9x
∴ 10 x + 15x + 9x = 68⇒ 34x = 68 ⇒ x = 68 = 2 34
∴ Second number = 15 x
= 15 × 2 = 30
