Ratio, Proportion
- Of three positive numbers, the ratio of 1st and 2nd is 8 : 9, that of 2nd and 3rd is 3:4. The product of 1st and 3rd is 2400. The sum of the three numbers is
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A : B = 8 : 9
B : C = 3 : 4 = 9 : 12
∴ A : B : C = 8 : 9 : 12
∴ Numbers = 8x, 9x and 12x
∴ 8x × 12x = 2400⇒ x2 = 2400 = 25 8 × 12
∴ x = √25 = 5
∴ A + B + C = 8x + 9x + 12x
= 29x
= 29 × 5 = 145Correct Option: A
A : B = 8 : 9
B : C = 3 : 4 = 9 : 12
∴ A : B : C = 8 : 9 : 12
∴ Numbers = 8x, 9x and 12x
∴ 8x × 12x = 2400⇒ x2 = 2400 = 25 8 × 12
∴ x = √25 = 5
∴ A + B + C = 8x + 9x + 12x
= 29x
= 29 × 5 = 145
- What number should be added to each of 6, 14, 18 and 38 so that the resulting numbers make a proportion ?
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6 + x = 18 + x 14 + x 38 + x
From the given alternatives6 + 2 = 18 + 2 14 + 2 38 + 2 ⇒ 1 = 1 2 2
Second Method :
Here, a = 6, b = 14, c = 18, d = 38Required number x = bc − ad (a + d) − (b + c) = 14 × 18 − 6 × 38 (6 + 38) − (14 + 18) = 252 − 228 44 − 32 = 24 = 2 12 Correct Option: B
6 + x = 18 + x 14 + x 38 + x
From the given alternatives6 + 2 = 18 + 2 14 + 2 38 + 2 ⇒ 1 = 1 2 2
Second Method :
Here, a = 6, b = 14, c = 18, d = 38Required number x = bc − ad (a + d) − (b + c) = 14 × 18 − 6 × 38 (6 + 38) − (14 + 18) = 252 − 228 44 − 32 = 24 = 2 12
- Which number when added to each of the numbers 6, 7, 15, 17 will make the resulting numbers proportional ?
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Let required number be x.
∴ 6 + x = 15 + x 7 + x 17 + x
⇒ 102 + 17x + 6x + x2
= 105 + 7x + 15x + x2
⇒ 23x – 22x = 105 – 102
⇒ x = 3
Note : It is convenient to solve it orally using options6 + 3 = 15 + 3 ⇒ 9 = 18 7 + 3 17 + 3 10 20
Second Method :Required Number = bc − ad (a + d) − (b + c)
Where a = 6, b = 7, c = 15, d = 17= 7 × 15 − 6 × 17 (6 + 17) − (7 + 15) = 105 − 102 = 3 23 − 22 Correct Option: D
Let required number be x.
∴ 6 + x = 15 + x 7 + x 17 + x
⇒ 102 + 17x + 6x + x2
= 105 + 7x + 15x + x2
⇒ 23x – 22x = 105 – 102
⇒ x = 3
Note : It is convenient to solve it orally using options6 + 3 = 15 + 3 ⇒ 9 = 18 7 + 3 17 + 3 10 20
Second Method :Required Number = bc − ad (a + d) − (b + c)
Where a = 6, b = 7, c = 15, d = 17= 7 × 15 − 6 × 17 (6 + 17) − (7 + 15) = 105 − 102 = 3 23 − 22
- Three numbers are in the ratio 3 : 4 : 5. The sum of the largest and the smallest equals the sum of the second and 52. The smallest number is
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Let the numbers be 3x, 4x and 5x.
∴ 5x + 3x = 4x + 52
⇒ 4x = 52 ⇒ x =13
∴ The smallest number
= 3x = 3 × 13 = 39Correct Option: C
Let the numbers be 3x, 4x and 5x.
∴ 5x + 3x = 4x + 52
⇒ 4x = 52 ⇒ x =13
∴ The smallest number
= 3x = 3 × 13 = 39
- If the sum of two quantities is equal to three times their difference, then the ratio of the two
quantities is
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x + y = 3 (x – y)
⇒ x + y = 3x – 3y Þ 2x = 4y⇒ x = 2 ⇒ x : y = 2 : 1 y 1 Correct Option: C
x + y = 3 (x – y)
⇒ x + y = 3x – 3y Þ 2x = 4y⇒ x = 2 ⇒ x : y = 2 : 1 y 1