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) 1536
(b) 1435
(c) 1256
(d) 1024
The correct answers to the above question in:
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
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Read more finding sum difference product problems Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
The ratio of number of boys to the number of girls in a school of 432 pupils is 5 : 4. When some new boys and girls are admitted, the number of boys increase by 12 and the ratio of the boys to girls changes to 7 : 6. The number of new girls admitted is
a) 24
b) 20
c) 14
d) 12
Answer »Answer: (a)
Original number of boys in school
= $5/9$ × 432 = 240
Number of girls
= 432 - 240 = 192
Let the new number of girls be x.
According to the question,
${240 + 12}/{192 + x} = 7/6$
$252/{192 + x} = 7/6$
192 × 7 + 7x = 252 × 6
1344 + 7x = 1512
7x = 1512 - 1344 = 168
$x = 168/7$ = 24
Question : 3
Two numbers are in the ratio 3 : 5. If each number is increased by 10, the ratio becomes 5 :7. The smaller number is
a) 15
b) 25
c) 12
d) 9
Answer »Answer: (a)
Let the numbers be 3x and 5x.
${3x + 10}/{5x + 10} = 5/7$
25x + 50 = 21x + 70
4x = 20 ⇒ x = 5
Smaller number
= 3x = 3 × 5 = 15
Using Rule 34,
Here, a = 3, b = 5, c = 5, d = 7, x = 10
Smallest number = ${xa(c-d)}/{ad-bc}$ a < b
= ${10 × 3(5 - 7)}/{3 × 7 - 5 × 5}$
= ${- 60}/{21 - 25} = 60/4$ = 15
Question : 4
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 : 5
Two numbers are in the ratio of 3 : 5. If 9 be subtracted from each, then they are in the ratio of 12 : 23. Find the numbers.
a) 33, 55
b) 60, 69
c) 36, 115
d) 15, 28
Answer »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
Question : 6
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
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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