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) 33, 55
(b) 60, 69
(c) 36, 115
(d) 15, 28
The correct answers to the above question in:
Answer: (a)
According to the question,
${3x - 9}/{5x - 9} = 12/23$
(Numbers = 3x and 5x )
69x - 207 = 60x - 108
9x = 207 - 108 = 99
x = 11
Required numbers
3 × 11 = 33 and 5 × 11 = 55
Using Rule 35,
Here, a = 3, b = 5, c = 12,
d = 23, x = 9
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
Numbers are 33, 55
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Read more finding sum difference product problems Based Quantitative Aptitude Questions and Answers
Question : 1
What number should be subtracted from both the terms of the ratio 11 : 15 so as to make it as 2 : 3 ?
a) 4
b) 5
c) 3
d) 2
Answer »Answer: (c)
Required number = x
${11 - x}/{15 - x} = 2/3$
33 - 3x = 30 - 2x
3x - 2x = 33 - 30
x = 3
Question : 2
If the ratio of two numbers is 1 : 5 and their product is 320, then the difference between the squares of these two numbers is :
a) 1536
b) 1435
c) 1256
d) 1024
Answer »Answer: (a)
Let the numbers be x and 5x.
According to the question,
x × 5x = 320
$5x^2$ = 320
$x^2 = 320/5$ = 64
$x = √64$ = 8
Required difference
= $(5x)^2 - x^2$
= $25x^2 - x^2 = 24x^2$
= 24 × 8 × 8 = 1536
Question : 3
What number should be added to or subtracted from each term of the ratio 17 : 24 so that it becomes equal to 1 : 2 ?
a) 7 is added
b) 10 is subtracted
c) 10 is added
d) 5 is subtracted
Answer »Answer: (b)
Let the number x be added.
${17 + x}/{24 + x} = 1/2$
34 + 2x = 24 + x
2x - x = 24 - 34
x = - 10
Hence, 10 should be subtracted.
Question : 4
Two numbers are in the ratio of 3 : 5. If 9 is subtracted from each then they are in the ratio 12 : 23. The smaller number is
a) 28
b) 36
c) 33
d) 55
Answer »Answer: (c)
Numbers = 3x and 5x (let)
According to question,
${3x - 9}/{5x - 9} = 12/23$
69x - 207 = 60x - 108
69x - 60x = 207 - 108
9x = 99 ⇒ $x = 99/9$ = 11
Smaller number = 3x = 3 × 11 = 33
Question : 5
A and B have money in the ratio Rs.2 : 1. If A gives 2 to B, the money will be in the ratio 1 : 1. What were the initial amounts they had?
a) Rs.8 and Rs.4
b) Rs.6 and Rs.3
c) Rs.16 and Rs.8
d) Rs.12 and Rs.6
Answer »Answer: (a)
Let A and B have Rs.2x and Rs.x initially.
2x - 2 = x + 2
x = 4
Initial amount with A = Rs.8
Initial amount with B = Rs.4.
Question : 6
If there is a reduction in the number of workers in a factory in the ratio 15 : 11 and an increment in their wage in the ratio 22 : 25, then the ratio by which the total wage of the workers should be decreased is
a) 3 : 7
b) 3 :5
c) 5 : 6
d) 6 : 5
Answer »Answer: (d)
Tricky Approach
Required ratio
= 15 × 22 : 11 × 25 = 6 : 5
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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