type 3 addition subtraction product on ratio & proportion Section-Wise Topic Notes With Detailed Explanation And Example Questions
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The following question based on ratio & proportion topic of quantitative aptitude
(a) 84
(b) 44
(c) 40
(d) 62
The correct answers to the above question in:
Answer: (b)
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
${124 - x + 2}/{x} =1/2$
252 - 2x = x
3x = 252 ⇒ x = 84
Smaller number
= 124 - 84 = 40
∴ Difference = 84 - 40 = 44
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Read more addition subtraction product on ratio and proportion Based Quantitative Aptitude Questions and Answers
Question : 1
The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is
a) 30
b) 20
c) 48
d) 49
Answer »Answer: (a)
Let the numbers be x, y and z.
Then x : y = 2 : 3 ; y : z = 5 : 8
x : y : z = 2 × 5 : 3 × 5 : 3 × 8
= 10 : 15 : 24
Sum of the ratios
= 10 + 15 + 24 = 49
The second number
= $15/49$ × 98 = 30
Question : 2
Three numbers are in the ratio of 3 : 2 : 5 and the sum of their squares is 1862. The smallest of these numbers is
a) 14
b) 35
c) 21
d) 24
Answer »Answer: (a)
Let the numbers be 3x, 2x and 5x respectively.
Now, $(3x)^2 + (2x)^2 + (5x)^2$ = 1862
$9x^2 + 4x^2 + 25x^2$ = 1862
$38x^2$ = 1862
$x^2 = 1862/38 = 49$
$x = √49 =7$
The smallest number
= 2x = 2 × 7 = 14
Question : 3
What number should be added to each of 6, 14, 18 and 38 so that the resulting numbers make a proportion ?
a) 3
b) 4
c) 2
d) 1
Answer »Answer: (c)
${6 + x}/{14 + x} ={18 +x}/{38 + x}$
From the given alternatives
${6 + 2}/{14 + 2} = {18 + 2}/{38 + 2}$
$1/2 = 1/2$
Using Rule 32,
Here, a = 6, b = 14, c = 18, d = 38
Required number x
= ${bc - ad}/{(a+d) - (b+c)}$
= ${14 × 18 - 6 × 38}/{(6 + 38) - (14 + 18)}$
= ${252 - 228}/{44 - 32}$
= $24/12$ = 2
Question : 4
Three numbers are in the ratio $1/2 : 2/3 : 3/4$. The difference between the greatest and the smallest number is 36. The numbers are
a) 72, 84, 96
b) 72, 96, 108
c) 60, 72, 96
d) 72, 84, 108
Answer »Answer: (b)
Ratio of numbers
= $1/2 : 2/3 : 3/4$
= $1/2 × 12 : 2/3 × 12 : 3/4 ×12$
= 6 : 8 : 9
Let the numbers be 6x, 8x and 9x.
Now, 9x - 6x = 36
x = 12
Numbers are 72, 96 and 108.
Question : 5
If the product of two positive numbers is 1575 and their ratio is 7 : 9, then the greater number is
a) 135
b) 63
c) 35
d) 45
Answer »Answer: (d)
Numbers = 7x and 9x (let)
According to the question,
7x × 9x = 1575
$x^2 = 1575/{7 × 9}$ = 25
$x = √25$ = 5
Larger number = 9x
= 9 × 5 = 45
Question : 6
The ratio of two numbers is 3 : 8 and their difference is 115. The smaller of the two numbers is :
a) 69
b) 59
c) 194
d) 184
Answer »Answer: (a)
Let the numbers be 3x and 8x.
8x - 3x = 115
5x = 115
$x = 115/5$ = 23
The smaller number
= 3x = 3 × 23 = 69
GET ratio & proportion PRACTICE TEST 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
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