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) 5
(b) 1
(c) 3
(d) 2
The correct answers to the above question in:
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
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Read more addition subtraction product on ratio and proportion Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
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 : 3
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 : 4
Two numbers are in the ratio of 2 : 3. If their sum is 125, find the numbers.
a) 20, 30
b) 32, 78
c) 24, 36
d) 50, 75
Answer »Answer: (d)
Ratio of numbers = 2 : 3
Sum of ratios = 2 + 3 = 5
First number = $2/5 × 125$ = 50
Second number = $3/5 × 125$ = 75
Question : 5
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
a) 30
b) 25
c) 20
d) 45
Answer »Answer: (c)
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
Question : 6
The product of two positive integers is 1575 and their ratio is 9 : 7. The smaller integer is
a) 45
b) 70
c) 35
d) 25
Answer »Answer: (c)
Let the integers be 9x and 7x respectively.
According to the question,
9x × 7x = 1575
$x^2 = 1575/63$
$x^2 = 25 ⇒ x = 5
[x being positive (+ve) integer]
Smaller integer
= 7x = 7 × 5 = 35
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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