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Ratio & Proportion Quiz For Upcoming Exams Answers

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Solution :-

1.(1) Ratio of amount collected
= (14 × 2) : (12 × 3) : (10 × 5)
= 28 : 36 : 50= 14 : 18 : 25
Sum of ratio = 14 + 18 + 25
= 57
∴ Amount colleted on day one
=14/57 × 4560 = Rs. 1120

2.(4) P’s present age = 8x years
Q’s present age = 5x years
After 4 years,
(8x + 4)/(5x + 4) = 4/3
= 24x + 12 = 20x + 16
= 24x – 20x = 16 – 12
= 4x = 4
x = 1
P’s age 7 years hence =8x + 7
= 8 + 7 = 15 years
Required ratio = 15 : 5 = 3 : 1

3.(2) Present age of younger child = x years
Present age of older child
= (x + 8) years
Sum of the present ages of 4 member family
= (4 × 40 + 4× 15) years
= (160 + 60) years = 220 years
Sum of present ages of 6 members
= 6 × 40 = 240 years
∴ Sum of the present ages of children
= 240 – 220 = 20 years
∴ x + x + 8 = 20
= 2x = 20 – 8 = 12
x = 6 years
∴ Present age of older child
= 6 + 8 = 14 years
∴ Required ratio= 14 : 6
= 7 : 3

4.(1) 4 years ago,
A’s age = 10 years,
B’s age = 3x years
∴ A’s present age
= (10x + 4) years
B’s present age = (3x + 4) years
According to the question,
(10x + 4 + 8)/2 – (3x + 4 + 8)
= – 2
= 3x + 12 – (5x + 6) = 2
= 3x + 12 – 5x – 6 = 2
= 5 – 2x = 2
= 2x = 6 – 2 = 4
x = 2
∴ B’s present age = 3x + 4
= 3 × 2 + 4 = 10 years

5.(5) Bob’s present age = x years (let)
∴ Abby’s present age
= (x + 8) years
According to the question,
After to the question, After 4 years
= (x + 4)/(x + 12) = 4/5
= 5x + 20 = 4x + 48
= 5x – 4x = 48 – 20
x = 28 years

6.(5) Total number of students in college A= 5x
Total number of students in college B = 8x
In college B,
Boys = 5/8 × 8x = 5x
Boys who study commerce
= 5x × 60/100 = 3x
Boys in other streams
= 5x- 3x =2x
∴ 2x = 800
x = 400
∴ Total number of students in college A
= 5x = 5 × 400 = 2000

7.(3) A : B = 3 : 4
A : C = 1 : 2 = 3 : 6
∴ A : B : C= 3 : 4 : 6
6 years hence,
3x + 4x + 6x + 18 = 96
= 13x = 96 – 18 = 78
= x = 78/13 = 6
∴ A’s present age
= 3x =18 years

8.(3) Let A’s present age be x years.
∴ B’s present age = (x+ 8) years
C’s present age = (x+ 16) years
After 12 years,
A’s age/ C’s age = 5/9
= (x +12)/(x+ 16 + 12)
= 5/9
= 9x + 108 = 5x + 140
= 9x – 5x = 140 – 108
= 4x = 32
x= 32/4 = 8
∴ Sum of the present age of A, B and C
= x + x + 8 + x + 16
= 3x + 24 = 3 × 8 + 24
= 48 years

9.(5) According to the question,
B = A + 3 = A = B – 3
and B = C – 3 = C = B + 3
Again, after 3 years, (B – 3 + 3)/(B + 3 + 3) = 4/5
= B/ B+ 6 = 4/5
= 5B = 4B + 24
= 5B – 4B = 24
= B = 24
∴ A + B + C
= B – 3 + B + B + 3
= 3B = 3 × 24 = 72 years

10.(5) Ranjana’s present age
= 15x years
Rakhi’s present age = 17x years
After 6 years,
(15x + 6)/(17x + 6) = 9/10
= 153x + 54 = 150x + 60
= 153x – 150x = 60 – 54
= 3x = 6
x= 2
∴ Ranjana’s age after 6 years
= 15x+ 6
= (15 × 2 + 6) years = 36 years

 

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