type 7 finding sum difference product based ratio & proportion problems 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) 100
(b) 114
(c) 76
(d) 95
The correct answers to the above question in:
Answer: (c)
Let the original number of students be 4x , 6x and 9x.
${4x + 12}/{6x +12} = 7/9$
42x + 84 = 36x + 108
42x - 36x = 108 - 84
6x = 24 ⇒ x = 4
Required number of students
= 19x = 19 × 4 = 76
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Read more finding sum difference product problems Based Quantitative Aptitude Questions and Answers
Question : 1
Two numbers are in the ratio 3 : 5. If 9 is subtracted from each, then they are in the ratio 12 : 23. Find the smaller number.
a) 49
b) 55
c) 33
d) 27
Answer »Answer: (c)
Let the numbers be 3x and 5x.
${3x - 9}/{5x - 9} = 12/23$
69x - 60x = 207 - 108
$x =99/9$ 11
The smaller number = 3x = 33
Using Rule 35,
Here, a = 3, b = 5, x= 9, c = 12, d = 23
1st Number = ${xa(d-c)}/{ad-bc}$
= ${9 ×3(23 - 12)}/{3 × 23 - 5 × 12}$
= ${27 × 11}/{69 - 60}$
=${27 × 11}/9$ = 33
2nd Number= ${xb(d-c)}/{ad-bc}$
= ${9 ×5(23 - 12)}/{3 × 23 - 5 × 12}$
= ${45 × 11}/{69 - 60}$
= ${45 × 11}/9$= 55
Smallest number = 33
Question : 2
Three numbers are in the ratio 1 : 2 : 3 and the sum of their cubes is 4500 . The smallest number is
a) 6
b) 10
c) 5
d) 4
Answer »Answer: (c)
Let the numbers be x, 2x and 3x.
According to the question,
$x^3 + (2x)^3 + (3x)^3$ = 4500
$x^3 + 8x^3 + 27x^3$ = 4500
$36x^3$ = 4500
$x^3 = 4500/36$ = 125
$x = √^3{125}$= 5 = smallest number
Question : 3
Two numbers are in the ratio 7 : 11. If 7 is added to each of the numbers, the ratio becomes 2 : 3. The smaller number is
a) 66
b) 77
c) 49
d) 39
Answer »Answer: (c)
Let the numbers be 7x and 11x respectively.
${7x + 7}/{11x + 7} = 2/3$
22x + 14 = 21x + 21
x = 7
Smaller number
= 7x = 7 × 7 = 49
Using Rule 34Two numbers are in the ratio a:b and if each number is increased by x, the ratio becomes c:d. Then the two numbers will be${xa(c-d)}/{ad-bc}$ and ${xb(c-d)}/{ad-bc}$
Here, a = 7, b = 11, x = 7, c= 2, d = 3
1st Number = ${xa(c-d)}/{ad-bc}$
= ${7 × 7(2 - 3)}/{7 × 3 - 11 × 2}$
= ${49 × -1}/{21 - 22}$ = 49
2nd Number = ${xb(c-d)}/{ad-bc}$
= ${7 × 11(2 - 3)}/{7 × 3 - 11 × 2}$
= ${77 × -1}/{21 - 22}$ = 77
Smallest number = 49
Question : 4
The ratio between two numbers is 2 : 3. If each number is increased by 4, the ratio between them becomes 5 : 7. The difference between the numbers is
a) 4
b) 2
c) 6
d) 8
Answer »Answer: (d)
Let the numbers be 2x and 3x.
${2x + 4}/{3x + 4} = 5/7$
15x + 20 = 14x + 28
x = 28 - 20 = 8
Required difference
Using Rule 34,
Here, a = 2, b = 3,c = 5
d = 7 and x = 4
1st Number = ${xa(c-d)}/{ad-bc}$
= ${4 ×2(5 - 7)}/{2 × 7 - 5 × 3}$
= ${8 × - 2}/{14 - 15}$ = 16
2nd Number= ${xb(c-d)}/{ad-bc}$
= ${4 ×3(5 - 7)}/{2 × 7 - 5 × 3}$
= ${4 × 3 (- 2)}/{14 - 15}$ = 24
Difference of numbers = 24 - 16 = 8
Question : 5
Two numbers are in the ratio 1$1/2 : 2{2}/3$. When each of these is increased by 15, they become in the ratio 1$2/3 : 2{1}/2$. The greater of the numbers is :
a) 48
b) 64
c) 36
d) 27
Answer »Answer: (a)
Let the numbers be $3/2$x and $8/3$x
According to question,
${3/2 x + 15}/{{8x}/3 + 15} = {5/3}/{5/2}$
${{3x + 30}/2}/{{8x + 45}/3} = 2/3$
${3(3x + 30)}/{2(8x + 45)} = 2/3$
${9x + 90}/{16x + 90} = 2/3$
27x + 270 = 32x + 180
32x - 27x = 270 - 180 = 90
5x = 90 ⇒ x = 18
The greater number
= $8/3 x = 8/3 × 18$ =48
Question : 6
The ratio of number of boys to that of girls in a group becomes 2:1 when 15 girls leave. But, afterwards, when 45 boys also leave, the ratio becomes 1 : 5. Originally the number of girls in the group was
a) 40
b) 50
c) 30
d) 20
Answer »Answer: (a)
Let the original number of boys and girls be x and y respectively.
Then $x/{y - 15} = 2/1$
x = 2y - 30 ....(i)
Again, ${x - 45}/{y - 15} =1/5$
5x - 225 = y - 15
5x = y - 15 + 225
5 (2y - 30) = y + 210
[From equation (i)]
10y - 150 = y + 210
10y - y = 210 + 150
9y = 360 ⇒ $y = 360/9$ = 40
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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