Ratio and Proportion Test

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Ratio and Proportion Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

If A : B = 5 : 6 and B : C = 8 : 9, Find A : B : C

A
5 : 6 : 27

B
$5: 6: \frac{27}{4}$

C
5 : 24 : 27

D
20 : 24 : 27

Solution

Given, $A: B=5: 6$
Multiplying it with $4,$ we get $A: B=20: 24$
And, $B: C=8: 9$
Multiplying it with $3,$ we get $A: B=24: 27$
In the given ratios "B" is the common term, and the values of B in both ratios are equal.
Therefore, $A: B: C=20: 24: 27$
Question 2
1 / -0

Two numbers are respectively 30%and 20% more than a thirdnumber. The ratio of the two numbers is

A
12:15

B
13:15

C
13:12

D
6:5

Solution

Let the third number be x.
First Number (130/100)x = 13x/10
Second Number (120/100)x = 12x/10
Ratio = 13x/10 : 12x/10
⇒ 13:12
Question 3
1 / -0

If $l: m=1 \frac{1}{2}: 1 \frac{1}{3}$ and $m: n=2 \frac{1}{3}: 4 \frac{1}{4}$ find $l: m: n$

A
36 : 20 : 51

B
30 : 28 : 51

C
36 : 28 : 50

D
36 : 28 : 51

Solution

$\frac{l}{m}=1 \frac{1}{2}: 1 \frac{1}{3}$
$\frac{l}{m}=\frac{\frac{3}{2}}{\frac{4}{3}}=\frac{3}{2} \times \frac{3}{4}=\frac{9}{8}$
$l=\frac{9}{8} m$
$\frac{m}{n}=2 \frac{1}{3}: 4 \frac{1}{4}$
$=\frac{\frac{7}{3}}{\frac{17}{4}}=\frac{7}{3} \times \frac{4}{17}=\frac{28}{51}$
$m=\frac{28}{51} n$
$n=\frac{51}{28} m$
$l: m: n=\frac{9}{8} m: m: \frac{51}{28} m$
$=\frac{9}{8}: 1: \frac{9}{8} \times 56: 56: \frac{51}{28} \times 56$
$=72: 56: 102$
$=36: 28: 51$
Hence, the correct option is (D).
Question 4
1 / -0

In a college, the ratio of the number of boys to girls is 16 : 10. If there are 250 girls, the total number of students in the college is

A
420

B
650

C
520

D
720

Solution

Given ratio = 16 : 10 = 8 : 5
the boy are 8x and Girls are 5x
⇒ 5x = 250
⇒ x = 50
Total students = 8x+5x = 13x = 13(50) = 650
Question 5
1 / -0

The least whole number which when subtracted from both the terms of the ratio $12 : 14$ to give a ratio less than $32 : 42$ , is

A
$3$

B
$4$

C
$5$

D
$6$

Solution

Given ratio are,
$12 : 14 = 6 : 7$ and $32 : 42 = 16 : 21$
Let x is subtracted.
Then,
$\frac{(6 - x)}{(7 - x)} < \frac{16}{21}$
$21 (6 - x) < 16 (7 - x)$
$5 x > 14$
$x > 2.8$
Least such number is $3$ .
Hence, the correct option is (A).
Question 6
1 / -0

$15: 65:: ?: 130$

A
30

B
35

C
130

D
222

Solution

Given $15: 65:: ?: 130$
So, the missing term $=\frac{15 \times 130}{65}=30$
Question 7
1 / -0

Find the fourth proportion to 2,3,6

A
18

B
12

C
9

D
4

Solution

2 : 3 :: 6 : x
⇒ 2/3 = 6/x
⇒ x = 18/2
⇒ x = 9
Question 8
1 / -0

Jaggu takes 2 leaps for every 3 leaps of monty. If one leap of the Jaggu is equal to 4 leaps of the Monty, the ratio of the speed of the Jaggu to that of the Monty is

A
4 : 5

B
8 : 3

C
8 : 5

D
9 : 2

Solution

Jaggu : Monty = (2 x 4) leaps of Monty : 3 leaps of Monty
= 8 : 3
Question 9
1 / -0

If Rs. 1564 is divided into three parts, proportional to 12:24:34. find the first part.

A
190

B
408

C
220

D
230

Solution

12 : 24 : 34 = 6 : 8 : 9
6x + 8x+ 9x = 1564
23x =1564
x = 68
Firstpart = 68 x 6
= 408.
Question 10
1 / -0

Two numbers are respectively 10% and 40% more than a third number. The ratio of the two numbers is

A
22:55

B
66:77

C
55:77

D
66:77

Solution

Let the third number be a.
First Number (110/100)xa = 11a/10
Second Number (140/100)xa = 7a/5
Ratio = 11a/10 : 7a/5
⇒ 55 : 77
Question 11
1 / -0

If three numbers in the ratio 6 : 4: 10 be such that the sum of their squares is 1862, the middle number will be

A
10

B
14

C
1

D
22

Solution

Given ratio = 6:4:10= 3:2:5
thenumbers be 3x, 2x and 5x.
Then,
9x + 4x + 25x =1862
⇒ 38x = 1862
⇒ x = 49 ⇒ x= 7.
middle number = 2x = 14
Question 12
1 / -0

If $b c: a c: a b=1: 2: 3,$ then find $\frac{a}{b c}: \frac{b}{c a}$

A
1 : 4

B
3 : 4

C
1 : 3

D
4 : 1

Solution

$b c: a c=1: 2$ or $a c: b c=2: 1$ or $a: b=2: 1(1)$
$a c: a b=2: 3$ or $a b: a c=3: 2$ or $b: c=3: 2(2)$
From (1) and (2), $a: b=2 \times 3: 1 \times 3=6: 3$
$\therefore a: b: c=6: 3: 2$
$\therefore \frac{a}{b c}: \frac{b}{c a}=\frac{6}{3 \times 2}: \frac{3}{2 \times 6}=1: \frac{1}{4}=4: 1$
Question 13
1 / -0

In a school the total number of students are 3200 out of which 1800 are boys. Remaining are girls. Ratio of girls to boys is

A
1400 : 1800

B
9 : 7

C
7 : 9

D
1 : 3

Solution

Total students = 3200
Boys = 1800
Girls = 1400
Ratio of girls to boys = 1400 : 1800 = 7 : 9
Question 14
1 / -0

Rs. 120 are divided among Amit, Bittu and Cheery such that Amit's shareis Rs. 20 more than Bittu's and Rs. 20 less than Cherry's. What is Bittu'sshare

A
Rs 10

B
Rs 20

C
Rs 24

D
Rs 28

Solution

Let Cherry = x.
Then Amit = (x-20) and Bittu = (x-40).
x + x - 20 + x - 40 = 120 Or x = 60.
Amit : Bittu : Cherry = 40 : 20 : 60 = 2 : 1 : 3
Bittu's share = Rs. 120x (1/6) = Rs. 20
Question 15
1 / -0

If 3 : 9 :: x : 9, then find the value of x

A
2

B
3

C
4

D
6

Solution

Treat 3 : 9 as 3/9 and x : 9 as x/9,
So we get
3/9 = x/9
⇒ 9x = 27
⇒ x = 3

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Ratio and Proportion Test - 4

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Ratio and Proportion Test - 4

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Question 1

5 : 6 : 27

\(5: 6: \frac{27}{4}\)

5 : 24 : 27

20 : 24 : 27

Solution

Question 2

12:15

13:15

13:12

6:5

Solution

Question 3

36 : 20 : 51

30 : 28 : 51

36 : 28 : 50

36 : 28 : 51

Solution

Question 4

420

650

520

720

Solution

Question 5

3

4

5

6

Solution

Question 6

30

35

130

222

Solution

Question 7

18

12

9

4

Solution

Question 8

4 : 5

8 : 3

8 : 5

9 : 2

Solution

Question 9

190

408

220

230

Solution

Question 10

22:55

66:77

55:77

66:77

Solution

Question 11

10

14

1

22

Solution

Question 12

1 : 4

3 : 4

1 : 3

4 : 1

Solution

$3$

$4$

$5$

$6$