Ratio and Proportion Formulas, Questions and Study Material

Ratio and Proportion Formulas

Ratio: The ratio of two quantities a and b in the same units, is the fraction $\frac{a}{b}$ and we write it as a : b.
In the ratio a : b, we call a as the first term or antecedent and b, the second term or consequent.

Example: The ratio 5 : 9 represents $\frac{5}{9}$ with antecedent = 5, consequent = 9.

Rule: The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio.
Eg. 4 : 5 = 8 : 10 = 12 : 15. Also, 4 : 6 = 2 : 3.

Proportion: The equality of two ratios is called proportion.
If a : b = c : d, we write a : b :: c : d and we say that a, b, c, d are in proportion.
Here a and d are called extremes, while b and c are called mean terms.

Product of means = Product of extremes.
Thus, a : b :: c : d $\Leftrightarrow$ (b x c) = (a x d).

Fourth Proportional: If a : b = c : d, then d is called the fourth proportional to a, b, c.

Third Proportional: a : b = c : d, then c is called the third proportion to a and b.

Mean Proportional: Mean proportional between a and b is ab.

Comparison of Ratios: We say that (a : b) > (c : d) $\Leftrightarrow$ $\frac{a}{b}>\frac{c}{d}$

Compounded Ratio: The compounded ratio of the ratios: (a : b), (c : d), (e : f) is (ace : bdf).

Duplicate Ratios: Duplicate ratio of (a : b) is ( $a^{2}$ : $b^{2}$ ).

Sub-duplicate ratio of (a : b) is (a : b).
Triplicate ratio of (a : b) is $a^{3}$ : $b^{3}$ )..
Sub-triplicate ratio of (a : b) is $a^{\frac{1}{3}}\, :\, b^{\frac{1}{3}}$
If $\frac{a}{b}\, =\frac{c}{d}$ , then $\frac{a\,+\,b}{a\,-\,b}\, =\,\frac{c\,+\,d}{c\,-\,d}$ [componendo and dividendo]

Variations: We say that x is directly proportional to y, if x = ky for some constant k and we write, x ∞ y.
We say that x is inversely proportional to y, if xy = k for some constant k and we write, x ∞ $\frac{1}{y}$

Ratio and Proportion Important Examples

Example: 1. A and B together have Rs. 1210. If $\frac{4}{15}$ of A's amount is equal to $\frac{2}{5}$ f B's amount, how much amount does B have?
Answer: 484
Explanation: $\frac{14}{5}A =\frac{2}{5}B$
$\Rightarrow A = \left ( \frac{2}{5}\times \frac{15}{4} \right ) B$
$\Rightarrow A = \frac{3}{2}B$
$\Rightarrow \frac{A}{B}B = \frac{3}{2}B$
$\Rightarrow A : B = 3 : 2.$
$\therefore$ B's share = Rs. $\left ( 1210x^{2} \right )= 484$

Example 2: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
Answer: 2000
Explanation: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 1000
$\Rightarrow$ x = 1000.
$\therefore$ B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.

Example 3: Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
Answer: 2 : 3 : 4
Explanation: Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
$\left ( \frac{140}{100}\times 5x \right )\, ,\left ( \frac{150}{100}\times 7x \right )\, ,\left ( \frac{175}{100}\times 8x \right )$
$7x,\,\frac{21x}{2}\,and\,14x.$
$\therefore$ The required ratio = $7x\,:\,\frac{21x}{2}\,:\,14x.$
$\Rightarrow$ 14x : 21x : 28x
$\Rightarrow$ 2 : 3 : 4

Example 4: In a mixture 60 litres, the ratio of milk and water 2 : 1. If the this ratio is to be 1 : 2, then the quantity of water to be further added is:
Answer: 60 litres.
Explanation: Quantity of milk = $\left ( 60\times\frac{2}{3}\right )$ litres = 40 litres.
Quantity of water in it = (60- 40) litres = 20 litres.
New ratio = 1 : 2
Let quantity of water to be added further be x litres.
Then, milk : water = $\frac{40}{20 + x}\, =\, \frac{1}{2}$
$\Rightarrow$ 20 + x = 80
$\Rightarrow$ x = 60.
$\therefore$ Quantity of water to be added = 60 litres.

Ratio and Proportion Questions from Previous Year Exams

IBPS Questions Related to Ratio and proportion.

Question 1 of 32

1. Question
1 points
The ratio of students of three classes is 2:3:4. If 12 students are increased in each classes then their ratio turns into 8:11:14. What was the total number of students in all the three classes originally?
- 162
- 108
- 96
- 54
Correct

Let the original number of student be 2x, 3x and 4x in three class.

According to question,

$\frac{2x+12}{3x+12}=\frac{8}{11}$

$\Rightarrow$ 11(2x + 12) = 8(3x + 12)

$\Rightarrow$ 22x + 132 = 24x + 96

$\Rightarrow$ 132 - 96 = 24x - 22x

$\Rightarrow$ 36 = 2x

$\Rightarrow$ x = 18

original number of student

2x + 3x + 4x = 9x = $9\times 18$ = 162

Incorrect

Let the original number of student be 2x, 3x and 4x in three class.

According to question,

$\frac{2x+12}{3x+12}=\frac{8}{11}$

$\Rightarrow$ 11(2x + 12) = 8(3x + 12)

$\Rightarrow$ 22x + 132 = 24x + 96

$\Rightarrow$ 132 - 96 = 24x - 22x

$\Rightarrow$ 36 = 2x

$\Rightarrow$ x = 18

original number of student

2x + 3x + 4x = 9x = $9\times 18$ = 162
Question 2 of 32

2. Question
1 points
If a:b = 2 : 3 and b:c = 4 : 5, then find a:b:c
- 2 : 4 : 5
- 2 : 3 : 8
- 2 : 3 : 9
- 2 : 3 : 12
Correct

a : b = 2 : 3 => $\frac{a}{b}=\frac{2}{3}=\frac{2\times 4}{3\times 4}=\frac{8}{12}=\frac{2}{3}$ [Multiplying numerator & denominator by 4]

so, $\frac{b}{a}=\frac{12}{8}$ i.e. we can write, b : a = 4 : 2 .....(i)

b : c = 4 : 5 => $\frac{b}{c}=\frac{4}{5}=\frac{4\times 3}{5\times 3}=\frac{12}{15}=\frac{4}{5}$ [multiplying numerator & denominator by 3]

So $\frac{c}{b}=\frac{5}{4}$ i.e. we can write, c : b = 5 : 4 ......(ii)

Now, from (i) & (ii), we can get,
c : b : a = 5 : 4 : 2

a : b : c = 2 : 4 : 5

Incorrect

a : b = 2 : 3 => $\frac{a}{b}=\frac{2}{3}=\frac{2\times 4}{3\times 4}=\frac{8}{12}=\frac{2}{3}$ [Multiplying numerator & denominator by 4]

so, $\frac{b}{a}=\frac{12}{8}$ i.e. we can write, b : a = 4 : 2 .....(i)

b : c = 4 : 5 => $\frac{b}{c}=\frac{4}{5}=\frac{4\times 3}{5\times 3}=\frac{12}{15}=\frac{4}{5}$ [multiplying numerator & denominator by 3]

So $\frac{c}{b}=\frac{5}{4}$ i.e. we can write, c : b = 5 : 4 ......(ii)

Now, from (i) & (ii), we can get,
c : b : a = 5 : 4 : 2

a : b : c = 2 : 4 : 5
Question 3 of 32

3. Question
1 points
What number should be subtracted from both the terms of the ratio 15 : 19 so as to make it as 3 : 4 ?
- 3
- 6
- 5
- 9
Correct

Let x be subtracted in numerator and denominator .Then,

$\Rightarrow \frac{15-x}{19-x}=\frac{3}{4}$

$\Rightarrow$ 3(19 - x) = 4(15 - x)

$\Rightarrow$ 57 - 3x = 60 - 4x

$\Rightarrow$ -3x +4x = 60 - 57

$\Rightarrow$ x = 3

Incorrect

Let x be subtracted in numerator and denominator .Then,

$\Rightarrow \frac{15-x}{19-x}=\frac{3}{4}$

$\Rightarrow$ 3(19 - x) = 4(15 - x)

$\Rightarrow$ 57 - 3x = 60 - 4x

$\Rightarrow$ -3x +4x = 60 - 57

$\Rightarrow$ x = 3
Question 4 of 32

4. Question
1 points
Find the fourth proportion to 2,3,6
- 18
- 12
- 9
- 4
Correct

2:3 :: 6:x

$\frac{2}{3}=\frac{6}{x}$

$\Rightarrow x=\frac{18}{2}$

$\Rightarrow$ x = 9

Incorrect

2:3 :: 6:x

$\frac{2}{3}=\frac{6}{x}$

$\Rightarrow x=\frac{18}{2}$

$\Rightarrow$ x = 9
Question 5 of 32

5. Question
1 points
X, Y and Z share a sum of money in the ratio 7 : 8 : 16. If Z receives Rs. 27 more than X, then the total money shared was.
- Rs. 48
- Rs. 279
- Rs. 93
- Rs. 558
Correct

Let ,

x = 7x, y = 8x, z = 16x

$\Rightarrow$ 16x = 7x + 27

$\Rightarrow$ 9x = 27

$\Rightarrow$ x = 3

7x + 8x + 16x = 31x = $31\times 3$ = 93 Rs.

Incorrect

Let ,

x = 7x, y = 8x, z = 16x

$\Rightarrow$ 16x = 7x + 27

$\Rightarrow$ 9x = 27

$\Rightarrow$ x = 3

7x + 8x + 16x = 31x = $31\times 3$ = 93 Rs.
Question 6 of 32

6. Question
1 points
If A : B = 2 : 3, B : C = 4 : 5 and C : D = 6 : 7, then find the value of A : B : C : D
- 15 : 24: 3 0 : 35
- 16 : 24: 30 : 35
- 17 : 24 : 30 : 35
- 18 : 24 : 30 : 35
Correct

A : B = 2 : 3

B : C= 4 : 5= $\left (4\times \frac{3}{4}:5\times \frac{3}{4}\right)$

= $3:\frac{15}{4}$

C : D= 6 :7 = $\left (6\times \frac{15}{4}:7 \times \frac{15}{4}\right )$

$\frac{15}{4}:\frac{35}{8}$

A: B: C: D = 16 : 24: 30: 35

Incorrect

A : B = 2 : 3

B : C= 4 : 5= $\left (4\times \frac{3}{4}:5\times \frac{3}{4}\right)$

= $3:\frac{15}{4}$

C : D= 6 :7 = $\left (6\times \frac{15}{4}:7 \times \frac{15}{4}\right )$

$\frac{15}{4}:\frac{35}{8}$

A: B: C: D = 16 : 24: 30: 35
Question 7 of 32

7. Question
1 points
If 2 : 9 :: x : 18, then find the value of x
- 2
- 3
- 4
- 6
Correct

2 : 9 :: x : 18

$\Rightarrow \frac{2}{9}=\frac{x}{18}$

$\Rightarrow$ 36 = 9x

$\Rightarrow$ x = 4

Incorrect

2 : 9 :: x : 18

$\Rightarrow \frac{2}{9}=\frac{x}{18}$

$\Rightarrow$ 36 = 9x

$\Rightarrow$ x = 4
Question 8 of 32

8. Question
1 points
If a : b : c = 3 : 4 : 7, then ratio of (a+b+c) : c will be equal to
- 2 : 1
- 14 : 3
- 7 : 2
- 1 : 2
Correct

a: b: c= 3 : 4 : 7

(a+ b+ c) : c = (3 + 4 + 7 ) : 7 = 14 : 7 = 2 : 1

Incorrect

a: b: c= 3 : 4 : 7

(a+ b+ c) : c = (3 + 4 + 7 ) : 7 = 14 : 7 = 2 : 1
Question 9 of 32

9. Question
1 points
If a+b : b+c : c+a = 6 : 7 : 8 and a + b + c = 14, then the value of c is :
- 6
- 8
- 7
- 14
Correct

Given that a+b : b+c : c+a = 6 : 7 : 8 and a + b + c = 14, and c = ?

a+b = 6x . . . . . (1)

b+c = 7 x. . . . (2)

c+a = 8 x . . . . (3)

Adding equation (1) , (2) and (3) we get

$\Rightarrow$ (a+b + b +c + c+a) = 6x + 7x + 8 x

$\Rightarrow$ 2(a + b + c) = 21x

$\Rightarrow2\times 14$ = 21x [ $\because$ a + b + c = 14 (given)]

$\Rightarrow$ x = $\frac{4}{3}$

a + b = $6\times \frac{4}{3}=8$

Given that a + b + c = 14

(a + b) +c = 14

8 + c = 14

$\Rightarrow$ c = 14 - 8 = 6

Incorrect

Given that a+b : b+c : c+a = 6 : 7 : 8 and a + b + c = 14, and c = ?

a+b = 6x . . . . . (1)

b+c = 7 x. . . . (2)

c+a = 8 x . . . . (3)

Adding equation (1) , (2) and (3) we get

$\Rightarrow$ (a+b + b +c + c+a) = 6x + 7x + 8 x

$\Rightarrow$ 2(a + b + c) = 21x

$\Rightarrow2\times 14$ = 21x [ $\because$ a + b + c = 14 (given)]

$\Rightarrow$ x = $\frac{4}{3}$

a + b = $6\times \frac{4}{3}=8$

Given that a + b + c = 14

(a + b) +c = 14

8 + c = 14

$\Rightarrow$ c = 14 - 8 = 6
Question 10 of 32

10. Question
1 points
if x:y = 1:3, then find the value of (7x+3y):(2x+y)
- 14 : 5
- 15 : 5
- 16 : 5
- 17 : 5
Correct

x= 1 and y = 3 (Given)

put the value of x and y in given expression

(7x+3y):(2x+y)

= 7 + 9 : 2 + 3 = 16:5

Incorrect

x= 1 and y = 3 (Given)

put the value of x and y in given expression

(7x+3y):(2x+y)

= 7 + 9 : 2 + 3 = 16:5
Question 11 of 32

11. Question
1 points
The salaries of A, B, and C are in the ratio of 1 : 2 : 3. The salary of B and C together is Rs. 6000. By what percent is the salary of C more than that of A?
- 100%
- 300%
- 200%
- 600%
Correct

Let the salaries of A, B, C be x, 2x and 3x respectively.

Then , 2x + 3x = 6000

$\Rightarrow$ x = 1200.

As salary = Rs. 1200, Bs salary = Rs. 2400, and Cs salary Rs. 3600.

Excess of Cs salary over As = $\left [ \left(\frac{2400}{1200}\right )\times 100\right]$ = 200 %.

Incorrect

Let the salaries of A, B, C be x, 2x and 3x respectively.

Then , 2x + 3x = 6000

$\Rightarrow$ x = 1200.

As salary = Rs. 1200, Bs salary = Rs. 2400, and Cs salary Rs. 3600.

Excess of Cs salary over As = $\left [ \left(\frac{2400}{1200}\right )\times 100\right]$ = 200 %.
Question 12 of 32

12. Question
1 points
Rs. 730 were divided among A, B, C in such a way that if A gets Rs. 3, then B gets Rs. 4 and if B gets Rs. 3.50 then C gets Rs. 3. The share of B exceeds that of C by :
- Rs 30
- Rs 70
- Rs 40
- Rs 210
Correct

A : B = 3 : 4 and B : C = $\frac{7}{2}$ : 3 = $\frac{8}{7}\times \frac{7}{2}\times \frac{8}{7}\times 3$ = 4 : $\frac{24}{7}$

A : B : C = 3 : 4 : $\frac{24}{7}$ = 21 : 28 : 24.

Bs share = Rs. $\left[730\times \left(\frac{28}{73}\right)\right]$ = Rs 280.

C’s share = Rs $\left[730\times \left(\frac{24}{73}\right)\right]$ = Rs 240.

Difference of their shares = 40

Incorrect

A : B = 3 : 4 and B : C = $\frac{7}{2}$ : 3 = $\frac{8}{7}\times \frac{7}{2}\times \frac{8}{7}\times 3$ = 4 : $\frac{24}{7}$

A : B : C = 3 : 4 : $\frac{24}{7}$ = 21 : 28 : 24.

Bs share = Rs. $\left[730\times \left(\frac{28}{73}\right)\right]$ = Rs 280.

C’s share = Rs $\left[730\times \left(\frac{24}{73}\right)\right]$ = Rs 240.

Difference of their shares = 40
Question 13 of 32

13. Question
1 points
Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 15 times as heavy as water?
- 1 : 1
- 2 : 3
- 1 : 2
- 3 : 2
Correct

Incorrect

Let the weight of gold be x and that of copper is y.

Then from the above condition

$\Rightarrow$ 19x + 9y = 15(x + y)

$\Rightarrow$ 4x = 6y

$\frac{x}{y}=\frac{3}{2}$

Hence, the ratio of gold and copper should be taken is $\frac{3}{2}$
Question 14 of 32

14. Question
1 points
Divide Rs.1024 in the ratio 9 : 7?
- 576, 448
- 235, 365
- 123, 231
- none of these
Correct

Sum of terms = (9 + 7) = 16

First part = Rs $1024\times \frac{9}{16}$ = Rs 576

Second part = Rs $1024\times \frac{7}{16}$ = Rs 448

Incorrect

Sum of terms = (9 + 7) = 16

First part = Rs $1024\times \frac{9}{16}$ = Rs 576

Second part = Rs $1024\times \frac{7}{16}$ = Rs 448
Question 15 of 32

15. Question
1 points
If a : b = 2 : 3 and b : c = 5 : 7, find the value of a : b : c ?
- 10 : : 15 : 21
- 10 : 15 : 17
- 5 : 7 : 13
- 7 : 15 : 13
Correct

If a : b = 2 : 3 and b : c = 5 : 7, find a : b : c.

Therefore, a : b = 2 : 3 = 2 x 5 : 3 x 5 = 10 : 15.

b : C = 5 : 7 = 5 x 3 : 7 x 3 = 15 : 21.

Therefore, a : b : c = 10 : 15 : 21

Incorrect

If a : b = 2 : 3 and b : c = 5 : 7, find a : b : c.

Therefore, a : b = 2 : 3 = 2 x 5 : 3 x 5 = 10 : 15.

b : C = 5 : 7 = 5 x 3 : 7 x 3 = 15 : 21.

Therefore, a : b : c = 10 : 15 : 21
Question 16 of 32

16. Question
1 points
The prices of a scooter and a T.V. are in the ratio 7 : 5. If the scooter costs Rs. 8000 more than a T.V. set, then the price of a T.V. set is :
- Rs. 20,000
- Rs. 24,000
- Rs. 28,000
- Rs. 32,000
Correct

Let the prices of a scooter and a T.V. set be Rs. 7x and Rs. 5x respectively.

Then, 7x - 5x = 8000

2x = 8000

x = 4000

Price of a T.V. set = Rs. (5 $\times$ 4000) = Rs. 20000.

Incorrect

Let the prices of a scooter and a T.V. set be Rs. 7x and Rs. 5x respectively.

Then, 7x - 5x = 8000

2x = 8000

x = 4000

Price of a T.V. set = Rs. (5 $\times$ 4000) = Rs. 20000.
Question 17 of 32

17. Question
1 points
Rs. 120 are divided among A, B, C such that A's share is Rs. 20 more than B's and Rs. 20 less than C's. What is B's share
- Rs 10
- Rs 20
- Rs 24
- Rs 28
Correct

Let C = x. Then A = (x - 20) and B = (x - 40).
x + x - 20 + x - 40 = 120

$\Rightarrow$ x = 60.
A : B : C = 40 : 20 : 60 = 2 : 1 : 3.
B's share = Rs $120\times \frac{1}{6}$ = Rs 20

Incorrect

Let C = x. Then A = (x - 20) and B = (x - 40).
x + x - 20 + x - 40 = 120

$\Rightarrow$ x = 60.
A : B : C = 40 : 20 : 60 = 2 : 1 : 3.
B's share = Rs $120\times \frac{1}{6}$ = Rs 20
Question 18 of 32

18. Question
1 points
The ratio of income of A to that of B is 5 : 4 and the expenditure of A to that of B is 3: 2. If at the end of the year, each saves Rs, 800, the income of A is :
- Rs. 1600
- Rs. 2000
- Rs. 1800
- Rs. 2200
Correct

Let the income of A and B be 5x and 4x and. the expenditures of A and B be 3y and 2y.

Then, 5x—3y = 800 and 4x— 2y= 800.
On solving we get : x = 400. As income = 5x = Rs. 2000.

Incorrect
Question 19 of 32

19. Question
1 points
If 7 : x = 17.5 : 22.5 , then the value of x is:
- 9
- 6
- 7.5
- 5.5
Correct

$\frac{7}{x}=\frac{17.5}{22.5}$

$x=7\times \frac{22.5}{17.5}$ = 9

Incorrect

$\frac{7}{x}=\frac{17.5}{22.5}$

$x=7\times \frac{22.5}{17.5}$ = 9
Question 20 of 32

20. Question
1 points
Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is
- 2:5
- 3:5
- 4:5
- 6:5
Correct

Let the third number be x.

First Number $\frac{120}{100}\times x=\frac{6x}{5}$

Second Number $\frac{150}{100}\times x=\frac{3x}{2}$

Ratio = $\frac{6x}{5}:\frac{3x}{2}$ = 4 : 5

Incorrect

Let the third number be x.

First Number $\frac{120}{100}\times x=\frac{6x}{5}$

Second Number $\frac{150}{100}\times x=\frac{3x}{2}$

Ratio = $\frac{6x}{5}:\frac{3x}{2}$ = 4 : 5
Question 21 of 32

21. Question
1 points
What number should be added to each of the numbers 8, 21, 13 and 31 so that the resulting numbers, in this order form a proportion?
- 2
- 5
- 3
- 7
Correct

Let the number be x

(8+x)/(21+x) = (13+x)/(31+x)

Then, (8 + x)(31 + x) = (13 + x)(21 + x)

$\Rightarrow$ 39x + 248 = 34x + 273

$\Rightarrow$ 5x = 25 or x = 5.

Incorrect

Let the number be x

(8+x)/(21+x) = (13+x)/(31+x)

Then, (8 + x)(31 + x) = (13 + x)(21 + x)

$\Rightarrow$ 39x + 248 = 34x + 273

$\Rightarrow$ 5x = 25 or x = 5.
Question 22 of 32

22. Question
1 points
In a mixture 60 litres, the ratio of milk and water 2 : 1. If the this ratio is to be 1 : 2, then the quanity of water to be further added is
- 20 liters
- 30 liters
- 50 liters
- 60 liters
Correct

Quantity of Milk = $\Rightarrow 60\times \left(\frac{2}{3}\right)$ = 40 liters

Quantity of water = 60 - 40 = 20 liters

As per question we need to add water to get quantity 2 :1

=> $\frac{40}{20+x}=\frac{1}{2}$

=> 20 + x = 80

=> x = 60 liters

Incorrect

Quantity of Milk = $\Rightarrow 60\times \left(\frac{2}{3}\right)$ = 40 liters

Quantity of water = 60 - 40 = 20 liters

As per question we need to add water to get quantity 2 :1

=> $\frac{40}{20+x}=\frac{1}{2}$

=> 20 + x = 80

=> x = 60 liters
Question 23 of 32

23. Question
1 points
A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is
- 4:5
- 9:5
- 8:5
- 9:2
Correct

Dog : Hare = ( $3\times 3$ ) leaps of hare : 5 leaps of hare
= 9 : 5

Incorrect

Dog : Hare = ( $3\times 3$ ) leaps of hare : 5 leaps of hare
= 9 : 5
Question 24 of 32

24. Question
1 points
The ratio of zinc and copper in a brass pieces is 13 : 7. How much zinc will be there in 100 kg of such a piece?
- 55 kg
- 65 kg
- 75 kg
- 85 kg
Correct

Amount of zinc = $\left (100\times\frac{13}{20}\right)$ kg = 65 kg

Incorrect

Amount of zinc = $\left (100\times\frac{13}{20}\right)$ kg = 65 kg
Question 25 of 32

25. Question
1 points
The third proportional to 0.36 and 0.48 is :
- 0.64
- 0.1728
- 0.42
- 0.94
Correct

Incorrect

Let the third proportional to 0.36 and 0.48 be x

Then, 0.36 : 0.48 :: 0.48 : x

$\Rightarrow \left ( \frac{0.48\times 0.48}{0.36} \right )=0.64$
Question 26 of 32

26. Question
1 points
Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 28.8 kg of zinc has been consumed in it?
- 58 kg
- 60 kg
- 64 kg
- 70 kg
Correct

Incorrect

For 9 kg zinc, mixture melted = (9 + 11) kg.

For 28.8 kg zinc, mixture melted = $\left ( \frac{20}{9} \times 28.8\right )kg=64\, \, kg$
Question 27 of 32

27. Question
1 points
If 40% of a number is equal to two-third of another number, What is the ratio of first number to the second number?
- 2 : 5
- 3 : 7
- 5 : 3
- 7 : 3
Correct

Incorrect

Let 40% of A = $\frac{2}{3}B$

$Then,\, \, \, \frac{40A}{100}=\frac{2B}{3}$

$\Rightarrow \frac{2A}{5}=\frac{2B}{3}$

$\Rightarrow \frac{A}{B}=\left ( \frac{2}{3}\times \frac{5}{2} \right )=\frac{5}{3}$

$\therefore A:B=5:3$
Question 28 of 32

28. Question
1 points
The salaries of A, B and C are of ratio 2:3:5. If the increments of 15%, 10% and 20% are done to their respective salaries, then find the new ratio of their salaries.
- 20:33:60
- 21:33:60
- 22:33:60
- 23:33:60
Correct

Let A salary be 2x, B is 3x and C salary be 5x

A's new slary be= $\frac{115}{100}\times 2k=\frac{23}{10}k$

B's new slary be= $\frac{110}{100}\times 3k=\frac{33}{10}k$

C's new slary be= $\frac{120}{100}\times 5k=6k$

New ratio= $\frac{23}{10}k:\frac{33}{10}k:6k$

23: 33: 60

Incorrect

Let A salary be 2x, B is 3x and C salary be 5x

A's new slary be= $\frac{115}{100}\times 2k=\frac{23}{10}k$

B's new slary be= $\frac{110}{100}\times 3k=\frac{33}{10}k$

C's new slary be= $\frac{120}{100}\times 5k=6k$

New ratio= $\frac{23}{10}k:\frac{33}{10}k:6k$

23: 33: 60
Question 29 of 32

29. Question
1 points
In a college, the ratio of the number of boys to girls is 8 : 5. If there are 200 girls, the total number of students in the college is
- 420
- 520
- 620
- 720
Correct

Incorrect

Let the boy are 8x and Girls are 5x

=> 5x = 200
=> x = 40

Total students = 8x+5x = 13x = 13(40) = 520
Question 30 of 32

30. Question
1 points
If A : B = 3 : 4 and B : C = 8 : 9, then the ratio A : B : C is.
- 3 : 4 : 5
- 1 : 2 : 3
- 7 : 12 : 17
- 6 : 8 : 9
Correct

Incorrect

Here n1= 3, n2=8 and d1=4, d2=9

$\therefore a:b:c=\left ( n_{1} \times n_{2}\right ):\left ( d_{1} \times n_{2}\right ):\left ( d_{1} \times d_{2}\right )$

$3\times 8:4\times 8:4\times 9$

24: 32: 36= 6 : 8 : 9
Question 31 of 32

31. Question
1 points
Three containers have their volumes in the raito 3 : 4 : 5, They are full of mixtures of milk and water. The mixtures contain milk and water in the ratio of (4 : 1), (3 : 1) and (5 : 2) respectively. The contents of all these three containers are poured into a fourth container. The ratio of milk and water in the fourth container is :
- 4 : 1
- 151 : 48
- 157 : 53
- 5 : 2
Correct

Let the three containers contain 3x, 4x and 5x liters of mixtures respectively.

Milk in 1st mix. = $\left (3x\times \frac{4}{5}\right )liters=\frac{12x}{5}liters$

Water in 1st mix. = $\left (3x- \frac{12x}{5}\right )liters=\frac{3x}{5}liters$

Milk in 2nd mix. = $\left (4x\times \frac{3}{4}\right )liters=3x liters$

Water in 2nd mix. = $4x-3xliters=x liters$

Milk in 3rd mix. = $\left (5x\times \frac{5}{7}\right )liters=\frac{25x}{7}liters$

Water in 3rd mix. == $\left (5x-s \frac{25x}{7}\right )liters=\frac{10x}{5}liters$

Total milk in final mix. = $\left ( \frac{12x}{5} +3x+\frac{25x}{7}\right )liter=\frac{314x}{35}liters$

Total water in final mix. = $\left ( \frac{3x}{5} +x+\frac{10x}{7}\right )liter=\frac{106x}{35}liters$

Required ratio of milk and water = $\frac{314x}{35}:\frac{106x}{35}=157:53$

Incorrect

Let the three containers contain 3x, 4x and 5x liters of mixtures respectively.

Milk in 1st mix. = $\left (3x\times \frac{4}{5}\right )liters=\frac{12x}{5}liters$

Water in 1st mix. = $\left (3x- \frac{12x}{5}\right )liters=\frac{3x}{5}liters$

Milk in 2nd mix. = $\left (4x\times \frac{3}{4}\right )liters=3x liters$

Water in 2nd mix. = $4x-3xliters=x liters$

Milk in 3rd mix. = $\left (5x\times \frac{5}{7}\right )liters=\frac{25x}{7}liters$

Water in 3rd mix. == $\left (5x-s \frac{25x}{7}\right )liters=\frac{10x}{5}liters$

Total milk in final mix. = $\left ( \frac{12x}{5} +3x+\frac{25x}{7}\right )liter=\frac{314x}{35}liters$

Total water in final mix. = $\left ( \frac{3x}{5} +x+\frac{10x}{7}\right )liter=\frac{106x}{35}liters$

Required ratio of milk and water = $\frac{314x}{35}:\frac{106x}{35}=157:53$
Question 32 of 32

32. Question
1 points
The ratio of number of men and women in a factory of 720 workers is 7 : 5. How many more women should be joined to make the ratio 1 : 1?
- 100
- 120
- 200
- 220
Correct

Number of men = $70\times \frac{7}{12}$ = Number of women = (720 - 420) = 300.

∴ Number of women to be joined = (420 - 300) = 120.

Incorrect

Number of men = $70\times \frac{7}{12}$ = Number of women = (720 - 420) = 300.

∴ Number of women to be joined = (420 - 300) = 120.