type 3 addition subtraction product on ratio & proportion Practice Questions Answers Test with Solutions & More Shortcuts
ratio & proportion PRACTICE TEST [9 - EXERCISES]
type 1 basic concepts of ratio & proportion
type 2 age based ratio & proportion problems
type 3 addition subtraction product on ratio & proportion
type 4 income & expenditure based ratio & proportion problems
type 5 shares & partnership based ratio & proportion problems
type 6 fractions based ratio & proportion problems
type 7 finding sum difference product based ratio & proportion problems
type 8 alligation & mixtures based ratio & proportion problems
type 9 coins & rupees based ratio & proportion problems
Question : 6 [SSC CGL Prelim 2005]
Two numbers are in the ratio 2 : 3. If 2 is subtracted from the first and 2 is added to the second, the ratio becomes 1 : 2. The sum of the numbers is :
a) 24
b) 10
c) 28
d) 30
Answer »Answer: (d)
Let the number be 2x and 3x.
Then. ${2x -2}/{3x + 2} = 1/2$
4x - 4 = 3x + 2
x = 6
Sum of numbers = 5x
= 5 × 6 = 30
Question : 7 [SSC CPO S.I.2005]
Of the three numbers, the ratio of the first and the second is 8 : 9 and that of the second and third is 3 : 4. If the product of the first and third number is 2400, then the second number is :
a) 30
b) 55
c) 40
d) 45
Answer »Answer: (d)
Let the numbers be a, b and c.
Now, a : b = 8 : 9
b : c = 3 : 4
a : b : c
= 8 × 3 : 9 × 3 : 9 × 4
= 24 : 27 : 36 = 8 : 9 : 12
$a/8 = b/9 = c/12= k$
a = 8k, b = 9k, c = 12k
According to the question,
8k × 12k = 2400
$k^2 = 2400/{8 × 12}$ = 25
k = 5
Second number
= 9k = 9 × 5 = 45
Question : 8 [SSC CPO S.I.2007]
When a particular number is subtracted from each of 7, 9, 11 and 15, the resulting numbers are in proportion. The number to be subtracted is :
a) 3
b) 5
c) 2
d) 1
Answer »Answer: (a)
Let the number to be subtracted be x.
According to the question,
${7 - x}/{9 - x} ={11 - x}/{15 - x}$
Now, check through options
Clearly, putting x = 3,
Each ratio = $2/3$.
Note : Solve such questions orally by mental exercise.
Using Rule 32Let 'x' be a number which is subtracted from a, b, c and d to make them proportional, thenx = ${ad - bc}/{(a+d) - (b+c)}$Let 'x' be a number which is added to a, b, c and d to make them proportional, thenx = ${bc - ad}/{(a+d) - (b+c)}$Here, a, b, c and d should always be in ascending order.
The number will be x
= ${ad - bc}/{(a+d) - (b+c)}$
= ${7 × 15 - 9 × 11}/{(7 + 15) - (9 + 11)}$
= ${105 - 99}/{22 - 20} = 6/2$ = 3
Question : 9 [SSC CGL Prelim 2002]
Two numbers are in the ratio 5 : 7. On diminishing each of them by 40, they become in the ratio 17 : 27. The difference of the numbers is :
a) 137
b) 50
c) 52
d) 18
Answer »Answer: (b)
Let the two numbers are x and y.
According to the question,
$x/y = 5/7$
7x = 5y
7x - 5y = 0 ...(I)
Again, ${x - 40}/{y - 40} =17/27$
27x - 1080 = 17y - 680
27x - 17y = 1080 - 680
27x - 17y = 400 ...(II)
From (I) × 17 - (II) × 5, we have
119x | - | 85y | =0 |
135x | - | 85y | =2000 |
- | + | - |
-16x = -2000
x = 125
Putting the value of x in equation (I)
7 × 125 = 5y
$y = {7 × 125}/5$ = 175
Difference of the numbers
= 175 - 125 = 50
Using Rule 35Two numbers are in the ratio a:b and if x is subtracted from each number the ratio becomes c:d. The two numbers will be= ${xa(d-c)}/{ad-bc}$ and ${xb(d-c)}/{ad-bc}$
Here, a = 5, b = 7, x = 40
c = 17, d = 27
The two numbers are
= ${xa(d-c)}/{ad-bc}$
= ${40 ×5(27 - 17)}/{5 × 27 - 7 × 17}$
= ${200 × 10}/{135 - 119}$
= $2000/16 = 500/4$
1st Number = 125
And = ${xb(d-c)}/{ad-bc}$
= ${40 ×7(27 - 17)}/{5 × 27 - 7 × 17}$
= ${280 × 10}/{135 - 119}$
= $2800/16 = 700/4$
2nd Number = 175
Their difference= 175 - 125 = 50
Question : 10 [SSC CGL Tier-I 2016]
The sum of three numbers is 540. The ratio of second to third is 9 : 13 and that of first to third is 2 : 7. The third number is :
a) 250
b) 286
c) 280
d) 273
Answer »Answer: (d)
Let three numbers be a, b and c respectively.
According to the question,
a + b + c = 540
and b : c = 9 : 13
a : c = 2 : 7
$a/c × c/b = 2/7 × 13/9$
$a/b = 26/63$
b : c = 9 : 13 = 63 : 91
a : b : c = 26 : 63 : 91
Sum of the terms of ratio
= 26 + 63 + 91 = 180
c = $91/180 × 540$ = 273
IMPORTANT quantitative aptitude EXERCISES
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199+ Ratio Proportion Basic Concepts MCQ Questions Answers »
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Top 199+ Ratio Proportion Age Based MCQ Questions Answers »
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159+ Ratios Proportions Addition Subtraction product MCQ »
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199+ Ratio Proportion Income, Expenditure Problems MCQS »
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199+ Partnership Aptitude (Ratio) MCQ Questions Answers »
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259+ Ratio and Proportion (fractions) Aptitude MCQ Quiz »
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199+ Ratio and Proportion Aptitude Questions Answers MCQ »
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299+ Alligation and Mixture Problems Aptitude MCQ Quiz »
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249+ Ratio and Proportion Coins Based Questions Answers »
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