Ratio, Proportion
- If two numbers are in the ratio 2 : 3 and the ratio becomes 3 : 4 when 8 is added to both
the numbers, then the sum of the two numbers is
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Let the numbers be 2x and 3x respectively.
According to the question,2x + 8 = 3 3x + 8 4
⇒ 9x + 24 = 8x + 32
⇒ 9x – 8x = 32 – 24 = 8
⇒ x = 8
∴ Sum of numbers = 2x + 3x
= 5x
= 5 × 8 = 40
Second Method :
Here, a = 2, b = 3, x= 8, c = 3, d = 41st Number = xa(c − d) ad − bc = 8 × 2(3 − 4) 2 × 4 − 3 × 3 = −16 = 16 −1 2nd Number = xa(c − d) ad − bc = 8 × 3(3 − 4) 2 × 4 − 3 × 3 = −24 = 24 −1
Sum of numbers = 16 + 24 = 40Correct Option: C
Let the numbers be 2x and 3x respectively.
According to the question,2x + 8 = 3 3x + 8 4
⇒ 9x + 24 = 8x + 32
⇒ 9x – 8x = 32 – 24 = 8
⇒ x = 8
∴ Sum of numbers = 2x + 3x
= 5x
= 5 × 8 = 40
Second Method :
Here, a = 2, b = 3, x= 8, c = 3, d = 41st Number = xa(c − d) ad − bc = 8 × 2(3 − 4) 2 × 4 − 3 × 3 = −16 = 16 −1 2nd Number = xa(c − d) ad − bc = 8 × 3(3 − 4) 2 × 4 − 3 × 3 = −24 = 24 −1
Sum of numbers = 16 + 24 = 40
- If A and B are in the ratio 4 : 5 and the difference of their squares is 81, what is the value of A ?
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Let A = 4x and B = 5x.
According to the question,
(5x)2 – (4x)2 81
⇒ 25x2 – 16x2 = 81
⇒ 9x2 = 81 ⇒ x2 = 9
⇒ x = √9 = 3
∴ A = 4x = 4 × 3 = 12Correct Option: B
Let A = 4x and B = 5x.
According to the question,
(5x)2 – (4x)2 81
⇒ 25x2 – 16x2 = 81
⇒ 9x2 = 81 ⇒ x2 = 9
⇒ x = √9 = 3
∴ A = 4x = 4 × 3 = 12
- If the product of two positive numbers is 1575 and their ratio is 7 : 9, then the greater number is
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Numbers = 7x and 9x (let)
According to the question,
7x × 9x = 1575⇒ x2 = 1575 = 25 7 × 9
⇒ x = √25 = 5
⇒ Larger number = 9x
= 9 × 5 = 45Correct Option: A
Numbers = 7x and 9x (let)
According to the question,
7x × 9x = 1575⇒ x2 = 1575 = 25 7 × 9
⇒ x = √25 = 5
⇒ Larger number = 9x
= 9 × 5 = 45
- The ratio of three positive numbers is 2 : 3 : 5 and the sum of their squares is 608. The three numbers are
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Numbers = 2x, 3x and 5x,
According to question,
(2x)2 + (3x)2 + (5x)2 = 608
⇒ 4x2 + 9x2 + 25x2 = 608
⇒ 38x2 = 608⇒ x2 = 608 = 16 38
⇒ x = √16 = 4
∴ Numbers ⇒ 2x = 2 × 4 = 8
3x = 3 × 4 = 12
5x = 5 × 4 = 20Correct Option: C
Numbers = 2x, 3x and 5x,
According to question,
(2x)2 + (3x)2 + (5x)2 = 608
⇒ 4x2 + 9x2 + 25x2 = 608
⇒ 38x2 = 608⇒ x2 = 608 = 16 38
⇒ x = √16 = 4
∴ Numbers ⇒ 2x = 2 × 4 = 8
3x = 3 × 4 = 12
5x = 5 × 4 = 20
- Two numbers are in the ratio of 2 : 3. If their sum is 125, find the numbers.
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∴ Ratio of numbers = 2 : 3
Sum of ratios = 2 + 3 = 5∴ First number = 2 × 125 = 50 5 Second number = 3 × 125 = 75 5 Correct Option: A
∴ Ratio of numbers = 2 : 3
Sum of ratios = 2 + 3 = 5∴ First number = 2 × 125 = 50 5 Second number = 3 × 125 = 75 5
