Ratio
Ratio represents the proportion in which a number contains another number. A ratio is represented by a/b or a:b. The duplication or division of every term of a proportion by the same non zero number does not influence the proportion.Subsequently, 3:5 is the same as 6:10 or 9:15 or 12:20 and so on.
Extent
The fairness of two proportions is called extent. As 2:3 = 6:9, we compose, 2:3::6:9 and we can say that 2,3,6,9 are in extent . Here 2 and 9 are called extremes while 3 and 6 are called implies.
In an extent, result of extremes=product of means.
Fourth Relative
if a:b::c:d, then d is known as the fourth relative to a,b and c.
Third Relative
if a:b::c:d, then c is known as the third relative to a and b.
Mean Relative
Mean relative is the middle of a and b.
Solved Examples
Answer - B
Explanation
We have a/b = 2/3 and b/c = 5/7 So a/c = (a/b*b/c) = (2/3*5/7) = 10/21 So its demonstrate that a:c = 10:21
Q 2 - On the off chance that a:b=2:3 and b:c=5:7, discover a:b:c.
Answer - A
Explanation
Here a/b = 2/3 and b/c = 5:7 = 3/5*5:3/5*7 = 3:21/5. So a:b=2:3 and b:c=3:21/5 So a:b:c = 2:3:21/5 = 10:15:21.
Q 3 - On the off chance that 4a = 5b and 8b = 9c, find a:b:c.
Answer - A
Explanation
4a = 5b => a/b=5/4 and 8b = 9c => b/c=9/8 So a:b = 5:4 and b:c = 9:8 = (4/9)(9):(4/9)(8) = 4:32/9 => a:b:c = 5:4:32/9 = 45:36:32. Hence,a:b:c = 45:36:32.
Answer - B
Explanation
Let a/8 = b/9 =c/12 =k. Then a=8k ,b=9k and c=12k. So a:b:c = 8k:9k:12k =8:9:12. Hence,a:b:c = 8:9:12.
Q 5 - In the event that a:b =1:3, b:c = 5:7 and c:d = 9:8 ,find a:b:c:d.
Answer - C
Explanation
We have a:b = 1:3, b:c = 5:7 and c:d = 9:8 => a:b = 5:15, b:c = 15:21, c:d =(21/9)*9 : (21/9)*8 => a:b = 5:15, b:c = 15:21, c:d = 21:56/3 => a:b:c:d =5:15:21:56/3 = 15:45:63:56 Consequently, a:b:c:d = 15:45:63:56
Answer - A
Explanation
Here (5x+3y)/(5x-3y) = 3/1 => 5x+3y = 15x-9y => 10x = 12y => x/y = 12/10 = 6/5 So x:y =6:5
Answer - D
Explanation
Given x/y = 5/3 Dividing numerator and denominator by y. (8x-5y)/(8x+5y) = {8(x/y) - 5}/{8(x/y) + 5} = {8*(5/3)-5}/{8*(5/3)+5} = (40-15)/(40+15) = 25/55 = 5/11 So (8x-5y):(8x+5y)= 5:11 Answer - D
Explanation
Let 4:5::12:x. => 4*x = (5*12) => x = 5*12/4 = 15 So the fourth relative to 4,5,12 is 15.
Answer - B
Explanation
Third relative to 9 and 12 is equivalent to fourth corresponding to 9,12 and 12. Give it a chance to be x at that point => 9:12::12:x => 9x = 12*12 => x = 12*12/9 =16 So the third relative is 16.
Answer - B
Explanation
Mean relative somewhere around 49 and 64 is 49*64 = (7*8) = 56.
Q 11 - An aggregate of rs. 391 has been divided between a,b,c in the proportion 1/2 :2/3:3/4 , discover the offer of each.
Answer - A
Explanation
We have a:b:c=1/2:2/3:3/4= 6:8:9. A share = (391*6/23) = 102 rs. B offer = (391*8/23) = 136 rs. C offer = (391*9/23) = 153 rs.
Q 12 - A sack contain one rupee, fifty paisa and 25 paisa in the proportion of 8:9:11, if the aggregate cash of the pack is 122, discover the no. of coins of every sorts.
Answer - A
Explanation
Let the quantity of one rupee, 50-p and 25-p coins be 8x, 9x and 11x individually. At that point, 8x + 9x/2 + 11x/4 =122 => 32x + 18x + 11x = 488 => 61x =488 => x = 8 No. of one rupee coins = 8*8= 64 No. of 50-p coins =9*8= 72 No. of 25-p coins =11*8 =88
Q 13 - A blend contains liquor and water in the proportion 4:3, if 7 liter of water is added to the blend, the proportion of liquor and water gets to be 3:4. Discover the amount of liquor in the blend.
Answer - B
Explanation
Let the amount of liquor and water be 4x liter and 3x liter separately. At that point , 4x/3x + 7 = 3/4 => 16x = 9x+21 => 7x = 21 so estimation of x is 3 Amount of liquor in the blend is = 4*3 =12 liters.
Q 14 - In a collection, the no. of understudy considering expressions, trade and science in the proportion of 4:7:9. On the off chance that the no. of understudy in expressions of the human experience, business and science be expanded by 30%, 20% and 40%. What will be the new proportion?
Answer - A
Explanation
Let the no. of understudy in expressions, business and science be 4x,7x and 9x individually. Presently they are 130% of 4x, 120 % of 7x and 140 % of 9x. Required proportion = (130/100*4x): (120/100*7x) (140/100*9x) =26x/5:42x/5:63x/5 =26:42:63.
Q 15 - The expense of assembling an auto is comprised of three items: cost of material, work and overheads. In a year, the expense of these things were in the proportion 4:3:2.Next year, the expense of material rose by 10%,cost of work expanded by 8% however the overheads lessened by 5%.Find the increment for every penny in the auto's cost.
Answer - A
Explanation
Let the expense of material, work and over head be rs. 4x, 3x and 2x separately. At that point aggregate expense =9x rs . New cost= {(110% of 4x) + (108% of 3x) +(90% of 2x)} ={(110/100*4x)+(108/100*3x)+(90/100*2x)} = (22x/5 + 81x/25 + 9x/5) = (110x+81x+45x)/25= 236x/25 Increment = {(236x/25)-9x} = 11x/25 Increase%= (11x/25)*(1/9x)*100 % = 44/9 % Q 16 - The proportion of no. of young men to that of the young ladies in a school is 3:2 .if 20% of young men and 25% of young ladies are grant holders, discover the % of the individuals who are not grant holders.
Answer - B
Explanation
Let the no. of young men be 3x and the no. of young ladies 2x. Aggregate no. = 5x No. of the individuals who are not grant holders = (80% of 3x)+(75% of 2x) = (80/100 * 3x) + ( 75/100 * 2x) = (12x/5 + 3x/2) = 39x/10 Required % = (39x/10)*(1/5x)*100 % = 78%
Q 17 - An and B together have rs.1210 with them. In the event that 4/15 of A sum is equivalent to 2/5 of B sum, what amount of sum does B have?
Answer - A
Explanation
Let (4/15)a = (2/5)b = x then a = 15x/4 and b = 5x/2 So. 15x/4 + 5x/2 =1210 => 15x + 10x = 4840 => 25x = 4840 => x=193.6 So. B = (5/2*193.6) = 484 Henceforth B has Rs. 484.
Answer - A
Explanation
(x + y)/(x - y)= 4/1 => x + y = 4x-4y => 3x = 5y => x/y = 5/3 Now (x2+y2)/ (x2-y2)= {(x/y)2+1}/ { (x/y )2-1 } = {(5/3)2+1} / {(5/2)2 -1} = 34/16 = 17/8 Answer - B
Explanation
(4x2 -3y2)/ (2x2 +5y2) = 12/19 =>76x2-57y2 = 24x2+60y2 => 52x2 = 117y2 => x2/y2 = 117/52 = 9/4 => (x/y)2=(3/2)2 => x/y = 3/2. => x:y = 3:2
Answer - A
Explanation
As x2+4y2 = 4xy => x2 + 4y2 - 4xy = 0 => (x-2y)2 = 0 => x-2y=0 => x = 2y => x/y = 2/1. => x:y = 2:1.
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