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 : 16 [SSC CGL Tier-I 2012]
The number to be added to each of the numbers 7, 16, 43, 79 to make the numbers in proportion is
a) 5
b) 1
c) 3
d) 2
Answer »Answer: (a)
From the given options number = 5, because
${7 + 5}/{16 + 5} = {43 + 5}/{79 + 5}$
$12/21 = 48/84$
[check other options likewise]
Using Rule 32,
Here, a = 7, b=16, c = 43, d= 79
Required number
x= ${bc - ad}/{(a+d) - (b+c)}$
= ${16 × 43 - 7 × 79}/{(7 + 79) - (16 + 43)}$
= ${688 - 553}/{86 - 79}$
= $35/7$ = 5
Question : 17 [SSC DEO 2009]
Which number when added to each of the numbers 6, 7, 15, 17 will make the resulting numbers proportional ?
a) 4
b) 3
c) 5
d) 6
Answer »Answer: (b)
Let required number be x.
${6 +x}/{7 + x} = {15 + x}/{17 + x}$
$102 + 17x + 6x + x^2$
= $105 + 7x + 15x + x^2$
23x - 22x = 105 - 102
x = 3
Note : It is convenient to solve it orally using options
${6 + 3}/{7 + 3} = {15 + 3}/{17 + 3}$
= $9/10 = 18/20$
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.
Required Number
= ${bc - ad}/{(a+d) - (b+c)}$
Where a = 6, b = 7, c = 15, d = 17
= ${7 × 15 - 6 × 17}/{(6 + 17) - (7 + 15)}$
= ${105 - 102}/{23 - 22}$ = 3
Question : 18 [SSC CGL Tier-I 2015]
If A and B are in the ratio 4 : 5 and the difference of their squares is 81, what is the value of A ?
a) 36
b) 15
c) 12
d) 45
Answer »Answer: (c)
Let A = 4x and B = 5x.
According to the question,
$(5x)^2 - (4x)^2$ = 81
$25x^2 - 16x^2$ = 81
$9x^2 = 81 ⇒ x^2$ = 9
$x = √9$ = 3
A = 4x = 4 × 3 = 12
Question : 19 [SSC CGL Tier-I 2010]
Two numbers are in the ratio 1 : 3. If their sum is 240, then their difference is
a) 100
b) 96
c) 108
d) 120
Answer »Answer: (d)
Let the numbers be 3x and x,
Then, 3x + x = 240
4x = 240
$x = 240/4$ = 60
Difference = 3x - x = 2x
= 2 × 60 = 120
Question : 20 [SSC CGL Tier-1 2011]
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
a) 39
b) 52
c) 27
d) 20
Answer »Answer: (a)
Let the numbers be 3x, 4x and 5x.
5x + 3x = 4x + 52
4x = 52 ⇒ x =13
The smallest number
= 3x = 3 × 13 = 39
IMPORTANT quantitative aptitude EXERCISES
-
199+ Ratio Proportion Basic Concepts MCQ Questions Answers »
-
Top 199+ Ratio Proportion Age Based MCQ Questions Answers »
-
159+ Ratios Proportions Addition Subtraction product MCQ »
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199+ Ratio Proportion Income, Expenditure Problems MCQS »
-
199+ Partnership Aptitude (Ratio) MCQ Questions Answers »
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259+ Ratio and Proportion (fractions) Aptitude MCQ Quiz »
-
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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