Quant quiz (Line Charts)

Directions to Solve

Study the following line graph and answer the questions.

1.	For which of the following pairs of years the total exports from the three Companies together are equal?
	A. 1995 and 1998 B. 1996 and 1998 C. 1997 and 1998 D. 1995 and 1996

2.	Average annual exports during the given period for Company Y is approximately what percent of the average annual exports for Company Z?
	A. 87.12% B. 89.64% C. 91.21% D. 93.33%

3.	In which year was the difference between the exports from Companies X and Y the minimum?
	A. 1994 B. 1995 C. 1996 D. 1997

4.	What was the difference between the average exports of the three Companies in 1993 and the average exports in 1998?
	A. Rs. 15.33 crores B. Rs. 18.67 crores C. Rs. 20 crores D. Rs. 22.17 crores

5.	In how many of the given years, were the exports from Company Z more than the average annual exports over the given years?
	A. 2 B. 3 C. 4 D. 5

6.	The incomes of two Companies X and Y in 2000 were in the ratio of 3:4 respectively. What was the respective ratio of their expenditures in 2000 ?
	A. 7:22 B. 14:19 C. 15:22 D. 27:35

7.	If the expenditure of Company Y in 1997 was Rs. 220 crores, what was its income in 1997 ?
	A. Rs. 312 crores B. Rs. 297 crores C. Rs. 283 crores D. Rs. 275 crores

8.	If the expenditures of Company X and Y in 1996 were equal and the total income of the two Companies in 1996 was Rs. 342 crores, what was the total profit of the two Companies together in 1996 ? (Profit = Income - Expenditure)
	A. Rs. 240 crores B. Rs. 171 crores C. Rs. 120 crores D. Rs. 102 crores

9.	The expenditure of Company X in the year 1998 was Rs. 200 crores and the income of company X in 1998 was the same as its expenditure in 2001. The income of Company X in 2001 was ?
	A. Rs. 465 crores B. Rs. 385 crores C. Rs. 335 crores D. Rs. 295 crores

10.	If the incomes of two Comapanies were equal in 1999, then what was the ratio of expenditure of Company X to that of Company Y in 1999 ?
	A. 6:5 B. 5:6 C. 11:6 D. 16:15

1 Answer: Option D

Explanation:

Total exports of the three Companies X, Y and Z together, during various years are:

In 1993 = Rs. (30 + 80 + 60) crores = Rs. 170 crores.

In 1994 = Rs. (60 + 40 + 90) crores = Rs. 190 crores.

In 1995 = Rs. (40 + 60 + 120) crores = Rs. 220 crores.

In 1996 = Rs. (70 + 60 + 90) crores = Rs. 220 crores.

In 1997 = Rs. (100 + 80 + 60) crores = Rs. 240 crores.

In 1998 = Rs. (50 + 100 + 80) crores = Rs. 230 crores.

In 1999 = Rs. (120 + 140 + 100) crores = Rs. 360 crores.

Clearly, the total exports of the three Companies X, Y and Z together are same during the years 1995 and 1996.

2 Answer: Option D

Explanation:

Analysis of the graph: From the graph it is clear that

1.    The amount of exports of Company X (in crore Rs.) in the years 1993, 1994, 1995, 1996, 1997, 1998 and 1999 are 30, 60, 40, 70, 100, 50 and 120 respectively.

2.    The amount of exports of Company Y (in crore Rs.) in the years 1993, 1994, 1995, 1996, 1997, 1998 and 1999 are 80, 40, 60, 60, 80, 100 and 140 respectively.

3.    The amount of exports of Company Z (in crore Rs.) in the years 1993, 1994, 1995, 1996, 1997, 1998 and 1999 are 60, 90,, 120, 90, 60, 80 and 100 respectively.

Average annual exports (in Rs. crore) of Company Y during the given period

=	1	x (80 + 40 + 60 + 60 + 80 + 100 + 140) =	560	= 80.
	7		7

Average annual exports (in Rs. crore) of Company Z during the given period

=	1	x (60 + 90 + 120 + 90 + 60 + 80 + 100) =		600		.
	7			7

Required percentage =		80	x 100		%  93.33%.
		600 7

3 Answer: Option C

Explanation:

The difference between the exports from the Companies X and Y during the various years are:

In 1993 = Rs. (80 - 30) crores = Rs. 50 crores.

In 1994 = Rs. (60 - 40) crores = Rs. 20 crores.

In 1995 = Rs. (60 - 40) crores = Rs. 20 crores.

In 1996 = Rs. (70 - 60) crores = Rs. 10 crores.

In 1997 = Rs. (100 - 80) crores = Rs. 20 crores.

In 1998 = Rs. (100 - 50) crores = Rs. 50 crores.

In 1999 = Rs. (140 - 120) crores = Rs. 20 crores.

Clearly, the difference is minimum in the year 1996.

4 Answer: Option C

Explanation:

Average exports of the three Companies X, Y and Z in 1993

= Rs.		1	x (30 + 80 + 60)		crores = Rs.		170		crores.
		3					3

Average exports of the three Companies X, Y and Z in 1998

= Rs.		1	x (50 + 100 + 80)		crores = Rs.		230		crores.
		3					3

Difference	= Rs. 230 - 170 crores 3 3
	= Rs. 60 crores 3
	= Rs. 20 crores.

5 Answer: Option C

Explanation:

Average annual exports of Company Z during the given period

=	1	x (60 + 90 + 120 + 90 + 60 + 80 + 100)
	7

= Rs.		600		crores
		7

    = Rs. 85.71 crores.

From the analysis of graph the exports of Company Z are more than the average annual exports of Company Z (i.e., Rs. 85.71 crores) during the years 1994, 1995, 1996 and 1999, i.e., during 4 of the given years.

6 Answer: Option C

Explanation:

Let the incomes in 2000 of Companies X and Y be 3x and 4x respectively.

And let the expenditures in 2000 of Companies X and Y be E₁ and E₂respectively.

Then, for Company X we have:

65 =	3x - E1	x 100	65	=	3x	- 1          E1 = 3x x		100		.... (i)
	E1		100		E1			165

For Company Y we have:

50 =	4x - E2	x 100	50	=	4x	- 1          E2 = 4x x		100		.... (ii)
	E2		100		E2			150

From (i) and (ii), we get:

E1	=	3x x 100 165	=	3 x 150	=	15	(Required ratio).
E2		4x x 100 150		4 x 165		22

7 Answer: Option B

Explanation:

Profit percent of Company Y in 1997 = 35.

Let the income of Company Y in 1997 be Rs. x crores.

Then, 35 =	x - 220	x 100          x = 297.
	220

 Income of Company Y in 1997 = Rs. 297 crores.

8 Answer: Option D

Explanation:

Let the expenditures of each companies X and Y in 1996 be Rs. x crores.

And let the income of Company X in 1996 be Rs. z crores.

So that the income of Company Y in 1996 = Rs. (342 - z) crores.

Then, for Company X we have:

40 =	z - x	x 100	40	=	z	- 1          x =	100z	.... (i)
	x		100		x		140

Also, for Company Y we have:

45 =	(342 -z)	x 100	45	=	(342 -z)	- 1     x=	(342 - z) x 100	.... (ii)
	x		100		x		145

From (i) and (ii), we get:

100z	=	(342 - z) x 100	z = 168.
140		145

Substituting z = 168 in (i), we get : x = 120.

 Total expenditure of Companies X and Y in 1996 = 2x = Rs. 240 crores.

Total income of Companies X and Y in 1996 = Rs. 342 crores.

 Total profit = Rs. (342 - 240) crores = Rs. 102 crores.

9 Answer: Option A

Explanation:

Let the income of Company X in 1998 be Rs. x crores.

Then, 55 =	x - 200	x 100          x = 310.
	200

Expenditure of Company X in 2001	= Income of Company X in 1998
	= Rs. 310 crores.

Let the income of Company X in 2001 be Rs. z crores.

Then, 50 =	z - 310	x 100          z = 465.
	310

 Income of Company X in 2001 = Rs. 465 crores.

10 Answer: Option D

Explanation:

Let the incomes of each of the two Companies X and Y in 1999 be Rs. x.

And let the expenditures of Companies X and Y in 1999 be E₁ and E₂respectively.

Then, for Company X we have:

50 =	x - E1	x 100	50	=	x	- 1          x =	150	E1 .... (i)
	E1		100		E1		100

Also, for Company Y we have:

60 =	x - E2	x 100	60	=	x	- 1          x =	160	E2 .... (ii)
	E2		100		E2		100

From (i) and (ii), we get:

150	E1 =	160	E2	E1	=	160	=	16	(Required ratio).
100		100		E2		150		15