Ratio, Proportion
- The sum of two numbers is equal to 20 and their difference is 25. The ratio of the two numbers is
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Numbers are x and y
∴ x + y = 25
x – y = 20
On adding,
2x = 45⇒ x = 45 = 22.5 2
From equation (i),
22.5 + y = 25
⇒ y = 25 - 22.5 = 2.5
∴ Required ratio = 22.5 : 2.5 = 9 : 1Correct Option: A
Numbers are x and y
∴ x + y = 25
x – y = 20
On adding,
2x = 45⇒ x = 45 = 22.5 2
From equation (i),
22.5 + y = 25
⇒ y = 25 - 22.5 = 2.5
∴ Required ratio = 22.5 : 2.5 = 9 : 1
- What number should be subtracted from both terms of the ratio 15 : 19 in order to make it
3 : 4 ?
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Let x be subtracted from each term of 15 . 19 ∴ 15 − x = 3 19 − x 4
⇒ 57 – 3x = 60 – 4x
⇒ x = 3Correct Option: D
Let x be subtracted from each term of 15 . 19 ∴ 15 − x = 3 19 − x 4
⇒ 57 – 3x = 60 – 4x
⇒ x = 3
- The average of two numbers is 62. If 2 is added to the smallest number, the ratio between the numbers becomes 1 : 2. The difference of the numbers is
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Average of two no's = 62
∴ Sum of the numbers
= 62 × 2 = 124
Sum of the numbers = 124
If the larger number be x, then
smaller number = 124 – x∴ 124 − x + 2 = 1 x 2
⇒ 252 – 2x = x
⇒ 3x = 252 ⇒ x = 84
∴ Smaller number = 124 – 84 = 40
∴ Difference = 84 – 40 = 44Correct Option: D
Average of two no's = 62
∴ Sum of the numbers
= 62 × 2 = 124
Sum of the numbers = 124
If the larger number be x, then
smaller number = 124 – x∴ 124 − x + 2 = 1 x 2
⇒ 252 – 2x = x
⇒ 3x = 252 ⇒ x = 84
∴ Smaller number = 124 – 84 = 40
∴ Difference = 84 – 40 = 44
- The number to be added to each of the numbers 7, 16, 43, 79 to make the numbers in proportion is
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From the given options number = 5, because
7 + 5 = 43 + 5 16 + 5 79 + 5 ⇒ 12 = 48 21 84
[check other options likewise]
Second Method :
Here, a = 7, b=16, c = 43, d= 79Required number x = bc − ad (a + d) − (b + c) = 16 × 43 − 7 × 79 (7 + 79) − (16 + 43) = 688 − 553 86 − 79 = 35 = 5 7 Correct Option: C
From the given options number = 5, because
7 + 5 = 43 + 5 16 + 5 79 + 5 ⇒ 12 = 48 21 84
[check other options likewise]
Second Method :
Here, a = 7, b=16, c = 43, d= 79Required number x = bc − ad (a + d) − (b + c) = 16 × 43 − 7 × 79 (7 + 79) − (16 + 43) = 688 − 553 86 − 79 = 35 = 5 7
- Three numbers are in the ratio 2 : 3 : 4. If the sum of their squares is 1856, then the numbers are
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Numbers = 2x, 3x and 4x
∴ (2x)2 + (3x)2 + (4x)2 = 1856
⇒ 4x2 + 9x2 +16x2 = 1856
⇒ 29x2 = 1856
⇒ x2 = 1856 ÷ 29 = 64
∴ x = √64 = 8
∴ Numbers = 16, 24 and 32Correct Option: B
Numbers = 2x, 3x and 4x
∴ (2x)2 + (3x)2 + (4x)2 = 1856
⇒ 4x2 + 9x2 +16x2 = 1856
⇒ 29x2 = 1856
⇒ x2 = 1856 ÷ 29 = 64
∴ x = √64 = 8
∴ Numbers = 16, 24 and 32
