Ratio, Proportion
- 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
- If the square of the sum of two numbers is equal to 4 times of their product, then the ratio of these numbers is :
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(x + y)2 = 4xy
⇒ x2 + y2 + 2xy – 4xy = 0
⇒ (x – y)2 = 0 ⇒ x = y
⇒ x : y = 1 : 1Correct Option: C
(x + y)2 = 4xy
⇒ x2 + y2 + 2xy – 4xy = 0
⇒ (x – y)2 = 0 ⇒ x = y
⇒ x : y = 1 : 1
- The ratio of number of balls in bags x,y is 2 : 3. Five balls are taken from bag y and are dropped in bag x. Number of balls are equal in each bag now. Number of balls in each bag now is
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Number of balls in bag x and y respectively = 2a and 3a
∴ 3a – 5 = 2a + 3
⇒ a = 5 + 3 = 8
∴ Total number of balls
= 5a = 40
∴ Balls in each bag = 20Correct Option: B
Number of balls in bag x and y respectively = 2a and 3a
∴ 3a – 5 = 2a + 3
⇒ a = 5 + 3 = 8
∴ Total number of balls
= 5a = 40
∴ Balls in each bag = 20
- The ratio between a two – digit number and the sum of the digits of that number is 4 : 1. If the digit at the unit’s place is 3 more than the digit at the ten's place, then the number is
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Check through options
Number = 36
3 + 6 = 9; 6 – 3 = 3
and 36 : 9 = 4 : 1
Otherwise– 10x + y : x + y = 4 : 1
⇒ 10x + (x + 3) : x + (x + 3) = 4 : 1⇒ 11x + 3 = 4 2x + 3 1
⇒ 11x + 3 = 8x + 12
⇒ 3x = 9 ⇒ x = 3 and y = 6
Then the number is 36.Correct Option: C
Check through options
Number = 36
3 + 6 = 9; 6 – 3 = 3
and 36 : 9 = 4 : 1
Otherwise– 10x + y : x + y = 4 : 1
⇒ 10x + (x + 3) : x + (x + 3) = 4 : 1⇒ 11x + 3 = 4 2x + 3 1
⇒ 11x + 3 = 8x + 12
⇒ 3x = 9 ⇒ x = 3 and y = 6
Then the number is 36.