Practice | Hashtable

51. The following table gives the percentage distribution of population of five states, P, Q, R, S and T on the basis of poverty line and also on the basis of sex. Study the table and answer the questions based on it.

State Percentage of Population Below Poverty Line Proportion of Males and Females

Below Poverty Line Above Poverty Line

M : F F : F

P 35 5 : 6 6 : 7

Q 25 3 : 5 4 : 5

R 24 1 : 2 2 : 3

S 19 3 : 2 4 : 3

T 15 5 : 3 3 : 2

If the male population above poverty line for state R is 1.9 million, then the total population of the state R is:

A. 4.5 million

B. 4.85 million

C. 5.35 million

D. 6.25 million

Discuss

Solution:

Let the total population of state R be x million.
Then, population of state R above poverty line
= [(100 - 24)% of x] million
=

(\frac{76}{100} \times x)

million
And so, male population of state R above poverty line

{\frac{2}{5} \times (\frac{76}{100} \times x)}

million
But, it is given that male population of state R above poverty line = 1.9 million

\begin{aligned} ∴ \frac{2}{5} \times (\frac{76}{100} \times x) = 1.9 \\ \Rightarrow x = \frac{5 \times 100 \times 1.9}{76 \times 2} \\ \Rightarrow x = 6.25 \end{aligned}

∴ Total population of state R = 6.25 million

52. The following table gives the percentage distribution of population of five states, P, Q, R, S and T on the basis of poverty line and also on the basis of sex. Study the table and answer the questions based on it.

State Percentage of Population Below Poverty Line Proportion of Males and Females

Below Poverty Line Above Poverty Line

M : F F : F

P 35 5 : 6 6 : 7

Q 25 3 : 5 4 : 5

R 24 1 : 2 2 : 3

S 19 3 : 2 4 : 3

T 15 5 : 3 3 : 2

If the population of males below poverty line for State Q is 2.4 million and that for State T is 6 million, then the total population of state Q and T are in the ratio:

A. 1 : 3

B. 2 : 5

C. 3 : 7

D. 4 : 9

Discuss

Solution:

For state Q:
Male population below poverty line = 2.4 million
Let the female population below poverty line be

x

million
Then,

\begin{aligned} 3 : 5 = 2.4 : x \\ \Rightarrow x = \frac{5 \times 2.4}{3} \\ \Rightarrow x = 4 \end{aligned}

∴ Total population below poverty line
= (2.4 + 4) million
= 6.4 million
Let the total population of Q be

p

Then,

\begin{aligned} 25 % of p = 6.4 million \\ \Rightarrow \frac{25}{100} \times p = 6.4 \\ \Rightarrow p = 6.4 \times 4 \\ \Rightarrow p = 25.6 million \end{aligned}

For state T:
Male population below poverty line = 6 million
Let the female population below poverty line be

y

million
Then,

\begin{aligned} 5 : 3 = 6 : y \\ \Rightarrow y = \frac{3 \times 6}{5} \\ \Rightarrow y = 3.6 \end{aligned}

∴ Total population below poverty line
= (6 + 3.6) million
= 9.6 million
Let the total population of state T be

q

Then,

\begin{aligned} 15 % of q = 9.6 million \\ \Rightarrow \frac{15}{100} \times q = 9.6 \\ \Rightarrow q = 9.6 \times \frac{20}{3} \\ \Rightarrow q = 64 million \\ ∴ Required ratio \\ = \frac{p}{q} \\ = \frac{25.6}{64} \\ = 0.4 \\ = \frac{4}{10} \\ = \frac{2}{5} \\ = 2 : 5 \\ So, the ratio of Q : T = 2 : 5 \end{aligned}

53. The following table gives the percentage distribution of population of five states, P, Q, R, S and T on the basis of poverty line and also on the basis of sex. Study the table and answer the questions based on it.

State Percentage of Population Below Poverty Line Proportion of Males and Females

Below Poverty Line Above Poverty Line

M : F F : F

P 35 5 : 6 6 : 7

Q 25 3 : 5 4 : 5

R 24 1 : 2 2 : 3

S 19 3 : 2 4 : 3

T 15 5 : 3 3 : 2

What will be the number of female above poverty line in the State S if it is known that the population of state S is 7 million?

A. 3 million

B. 2.43 million

C. 1.33 million

D. 5.7 million

Discuss

Solution:

Total population of state S = 7 million
∴ Population above poverty line
= {(100 - 19)% of 7} million
= (81% of 7) million
= 5.67 million
And so, the number of females above poverty line in state S

\begin{aligned} = (\frac{3}{7} \times 5.67) million \\ = 2.43 million \end{aligned}

54. The following table gives the percentage distribution of population of five states, P, Q, R, S and T on the basis of poverty line and also on the basis of sex. Study the table and answer the questions based on it.

State Percentage of Population Below Poverty Line Proportion of Males and Females

Below Poverty Line Above Poverty Line

M : F F : F

P 35 5 : 6 6 : 7

Q 25 3 : 5 4 : 5

R 24 1 : 2 2 : 3

S 19 3 : 2 4 : 3

T 15 5 : 3 3 : 2

What will be the male population above poverty line for State P if the female population below poverty line for State P is 2.1 million?

A. 2.1 million

B. 2.3 million

C. 2.7 million

D. 3.3 million

Discuss

Solution:

Female population below poverty line for state P = 2.1 million.
Let the male population below poverty line for state P be x million.
Then,

\begin{aligned} 5 : 6 = x : 2.1 \\ \Rightarrow \frac{x}{2.1} = \frac{5}{6} \\ \Rightarrow x = \frac{2.1 \times 5}{6} \\ \Rightarrow x = 1.75 \end{aligned}

∴ Population below poverty line for state P
= (2.1 + 1.75) million
= 3.85 million
Let the population above poverty line for state P be y million.
Since, 35% of the total population of state P is below poverty line, therefore 65% of the total population of state P is above poverty line. So, the ratio of population below poverty line to that above poverty line for state P is 35 : 65.

\begin{aligned} ∴ 35 : 65 = 3.85 : y \\ \Rightarrow y = \frac{65 \times 3.85}{35} \\ \Rightarrow y = 7.15 \end{aligned}

∴ Population above poverty line for state P = 7.15 million and so, male population above poverty line for state P

\begin{aligned} = (\frac{6}{13} \times 7.15) million \\ = 3.3 million \end{aligned}

55. Study the following table and answer the questions that are given below:
Expenditure of a Company (In Lakh Rupees) per Annum over the Given Years.

Items of Expenditure Salary Fuel and Transport Bonus Interest on Loans Taxes

Year ↓

2007 288 98 3.00 23.4 83

2008 342 112 2.52 32.5 108

2009 324 101 3.84 41.6 74

2010 336 133 3.68 36.4 88

2011 420 142 3.96 49.4 98

The total expenditure of the company over these items during the year 2009 is:

A. Rs. 544.44 lakhs

B. Rs. 501.11 lakhs

C. Rs. 446.46 lakhs

D. Rs. 478.87 lakhs

Discuss

Solution:

Total expenditure during 2009
= Rs. (324 + 101 + 3.84 + 41.6 + 74) lakh
= Rs. 544.44 lakh

56. Study the following table and answer the questions that are given below:
Expenditure of a Company (In Lakh Rupees) per Annum over the Given Years.

Items of Expenditure Salary Fuel and Transport Bonus Interest on Loans Taxes

Year ↓

2007 288 98 3.00 23.4 83

2008 342 112 2.52 32.5 108

2009 324 101 3.84 41.6 74

2010 336 133 3.68 36.4 88

2011 420 142 3.96 49.4 98

The total amount of bonus paid by the company during the given period is approximately what per cent of the total amount of salary paid during this period?

A. 0.1%

B. 0.5%

C. 1%

D. 1.25%

Discuss

Solution:

Total amount of bonus paid
= Rs. (3 + 2.52 + 3.84 + 3.68 + 3.96) lakh
= Rs. 17 lakh
Total Amount of salary paid
= Rs. (288 + 342 + 324 + 336 + 420) lakh
= Rs. 1710 lakh
∴ Required %

\begin{aligned} = (\frac{17}{1710} \times 100) % \\ = \frac{170}{171} % \\ = 0.99 % \\ \approx 1 % \end{aligned}

57. Study the following table and answer the questions that are given below:
Expenditure of a Company (In Lakh Rupees) per Annum over the Given Years.

Items of Expenditure Salary Fuel and Transport Bonus Interest on Loans Taxes

Year ↓

2007 288 98 3.00 23.4 83

2008 342 112 2.52 32.5 108

2009 324 101 3.84 41.6 74

2010 336 133 3.68 36.4 88

2011 420 142 3.96 49.4 98

What is the average amount of interest per year which the company had to pay during this period ?

A. Rs. 32.43 lakhs

B. Rs. 33.72 lakhs

C. Rs. 34.18 lakhs

D. Rs. 35.69 lakhs

Discuss

Solution:

Total amount of interest paid during the period
= Rs. (23.4 + 32.5 + 41.6 + 36.4 + 49.4) lakh
= Rs. 183.3 lakh
Average amount of interest paid per year
=

\frac{183.3}{5}

lakh
= Rs. 36.66 lakh

58. Study the following table and answer the questions that are given below:
Expenditure of a Company (In Lakh Rupees) per Annum over the Given Years.

Items of Expenditure Salary Fuel and Transport Bonus Interest on Loans Taxes

Year ↓

2007 288 98 3.00 23.4 83

2008 342 112 2.52 32.5 108

2009 324 101 3.84 41.6 74

2010 336 133 3.68 36.4 88

2011 420 142 3.96 49.4 98

The ratio between the total expenditure on Taxes for all the years and the total expenditure on Fuel and Transport for all the years respectively, is approximately :

A. 4 : 7

B. 10 : 13

C. 5 : 6

D. 5 : 8

Discuss

Solution:

Total expenditure on Taxes
= Rs. (83 + 108 + 74 + 88 + 98) lakh
= Rs. 451 lakh
Total expenditure of Fuel and Transport
= Rs. (98 + 112 + 101 + 133 + 142) lakh
= Rs. 586 lakh
∴ Required ratio

\begin{aligned} = \frac{451}{586} \\ = \frac{1}{1.3} \\ = \frac{10}{13} \\ = 10 : 13 \end{aligned}

59. Study the following table and answer the questions that are given below:
Expenditure of a Company (In Lakh Rupees) per Annum over the Given Years.

Items of Expenditure Salary Fuel and Transport Bonus Interest on Loans Taxes

Year ↓

2007 288 98 3.00 23.4 83

2008 342 112 2.52 32.5 108

2009 324 101 3.84 41.6 74

2010 336 133 3.68 36.4 88

2011 420 142 3.96 49.4 98

Total expenditure on all these items in 2007 was approximately what per cent of the total expenditure in 2011 ?

A. 62%

B. 66%

C. 69%

D. 71%

Discuss

Solution:

Total expenditure in 2007
= Rs. (288 + 98 + 3.00 + 23.4 + 83) lakh
= Rs. 495.4 lakh
Total expenditure in 2011
= Rs. (420 + 142 + 3.96 + 49.4 + 98) lakh
= Rs. 713.36 lakh
Let 495.4 = x % of 713.36
Then,

\begin{aligned} \Rightarrow \frac{x}{100} \times 713.36 = 495.4 \\ \Rightarrow x = \frac{495.40}{713.36} \times 100 \\ = \frac{12385}{17834} \times 100 \\ = 69.4 % \\ \approx 69 % \end{aligned}

60. Study the table carefully to answer the questions that follow:
Number of Boys and Girls (in Hundreds) in six different Years in 5 different Schools.

School → A B C D E

Year ↓ Boys Girls Boys Girls Boys Girls Boys Girls Boys Girls

2005 3.3 3.6 5.2 3.1 5.5 4.5 2.4 1.4 6.5 6.6

2006 6.6 4.2 4.9 2.2 6.9 3.3 4.4 2.3 5.5 3.6

2007 9.3 6.9 4.7 4.2 5.8 4.9 6.4 3.3 2.7 2.4

2008 5.4 9.6 6.3 5.4 6.6 5.2 5.3 5.4 5.4 5.7

2009 8.4 12.9 7.5 5.9 8.7 6.6 12.1 5.2 6.8 6.5

2010 12.3 14.4 9.8 4.4 11.7 4.2 12.2 9.4 10.8 12.7

The number of girls in school B in the year 2009 is approximately what percent of the total number of students in school E in the year 2006 ?

A. 46%

B. 52%

C. 70%

D. 58%

Discuss

Solution:

Number of girls in School B in 2009
= 5.9 × 100
= 590
Total Number of students in School E in 2006
= (5.5 + 3.6) × 100
= 9.1 × 100
= 910

\begin{aligned} Required % \\ = (\frac{590}{910} \times 100) % \\ = \frac{5900}{91} % \\ = 64.8 % \\ \approx 65 % \end{aligned}

State	Percentage of Population Below Poverty Line	Proportion of Males and Females
		Below Poverty Line	Above Poverty Line
		M : F	F : F
P	35	5 : 6	6 : 7
Q	25	3 : 5	4 : 5
R	24	1 : 2	2 : 3
S	19	3 : 2	4 : 3
T	15	5 : 3	3 : 2

Items of Expenditure	Salary	Fuel and Transport	Bonus	Interest on Loans	Taxes
Year ↓	Salary	Fuel and Transport	Bonus	Interest on Loans	Taxes
2007	288	98	3.00	23.4	83
2008	342	112	2.52	32.5	108
2009	324	101	3.84	41.6	74
2010	336	133	3.68	36.4	88
2011	420	142	3.96	49.4	98

School →	A		B		C		D		E
Year ↓	Boys	Girls	Boys	Girls	Boys	Girls	Boys	Girls	Boys	Girls
2005	3.3	3.6	5.2	3.1	5.5	4.5	2.4	1.4	6.5	6.6
2006	6.6	4.2	4.9	2.2	6.9	3.3	4.4	2.3	5.5	3.6
2007	9.3	6.9	4.7	4.2	5.8	4.9	6.4	3.3	2.7	2.4
2008	5.4	9.6	6.3	5.4	6.6	5.2	5.3	5.4	5.4	5.7
2009	8.4	12.9	7.5	5.9	8.7	6.6	12.1	5.2	6.8	6.5
2010	12.3	14.4	9.8	4.4	11.7	4.2	12.2	9.4	10.8	12.7