Line Charts Questions & Answers - Page 2

The percentage rise/fall in the number of students who left the school (compared to the previous year) during various years are:

For 1997 = [ (450 - 250)/250 x 100 ] % = 80% (rise).

For 1998 = [ (450 - 400)/450 x 100 ] % = 11.11% (fall).

For 1999 = [ (400 - 350)/400 x 100 ] % = 12.5% (fall).

For 2000 = [ (450 - 350)/350 x 100 ] % = 28.57% (rise).

For 2001 = [ (450 - 450)/450 x 100 ] % = 0%.

Clearly, the maximum percentage rise/fall is for 1997.

As calculated above, the number of students studying in the school during 1999 = 3150.

Amount received from Company Q after one year on investment of Rs. 5 lakhs in the year 1996

= Rs. [5 + (6.5% of 5)] lakhs

= Rs. 5.325 lakhs.

Amount received from Company P after one year on investment of Rs. 5.325 lakhs in the year 1997

= Rs. [5.325 + (9% of 5.325)] lakhs

= Rs. 5.80425 lakhs

= Rs. 5,80,425.

Amount received from Company P after one year (i.e., in 199) on investing Rs. 12 lakhs in it

= Rs. [12 + (8% of 12)] lakhs

= Rs. 12.96 lakhs.

Amount received from Company P after one year on investing Rs. 12.96 lakhs in the year 1999

= Rs. [12.96 + (10% of 12.96)] lakhs

= Rs. 14.256.

Appreciation received on investment during the period of two years

= Rs. (14.256 - 12) lakhs

= Rs. 2.256 lakhs

= Rs. 2,25,600.

Let Rs. x lakhs be invested in Company P in 2000, the amount invested in Company Q in 2000 = Rs. (30 - x) lakhs.

Total interest received from the two Companies after 1 year

= Rs. [(7.5% of x) + {9% of (30 - x)}] lakhs

= Rs. [ 2.7 - ( 1.5x/100 ) ] lakhs.

Therefore [ 2.7 - ( 1.5x/100 ) ] = 2.43 => x = 18.

Let the amounts invested in 2002 in Companies P and Q be Rs. 8x and Rs. 9x respectively.

Then, interest received after one year from Company P = Rs. (6% of 8x)

= Rs. (48/100) x.

and interest received after one year from Company Q = Rs. (4% of 9x)

= Rs. (36/100) x.

Therefore Required ratio = ( (48/100) x )/( (36/100) x ) = 4/3

Difference = Rs. [(10% of 4.75) - (8% of 4.75)] lakhs

= Rs. (2% of 4.75) lakhs

= Rs. 0.095 lakhs

= Rs. 9500.

We shall try to find the difference between the imports and exports of Company B for various years one by one:

For 1995: We have

E/I = 0.75

where E = amount of exports, I = amount of imports in 1995.

=> E = 0.75I

Therefore I - E = 0.75 x I = 0.25I.

Thus, the difference between the imports and exports of Company B in 1995 is dependent on the amount of imports of Company B in 1995.

Similarly, the difference for other years can be determined only if the amount of imports for these years is known.

Since the imports or exports for various years are not know, the differences between and exports for various years cannot be determined.

In 1995 for Company A we have:

E_A/I_A = 1.75 ... (i)

[where E_A = amount of exports, I_A = amount of imports of Company a in 1995]

In 1995 for Company B we have:

E_B/I_B = 0.75 ... (ii)

[where E_B = amount of exports, I_B = amount of imports of Company B in 1995]

Also, we have E_A = 2E_B ... (iii)

Substituting I_A = Rs. 180 crores (given) in (i), we get:

E_A = Rs. (180 x 1.75) crores = Rs. 315 crores.

Using E_A = Rs. 315 crores in (iii), we get:

E_B = E_A/2 = Rs. ( 315/2 ) crores. 

Substituting E_B = Rs. ( 315/2 ) crores in (ii), we get:

I_B = E_B/0.75 = Rs. ( 315/(2 x 0.75) ) crores = Rs. 210 crores.

i.e., amount of imports of Company B in 1995 = Rs. 210 crores.

Let the amount of imports of Company A in 1998 be Rs. x crores.

Then, 237/x = 0.75    =>    x = 237/0.75 = 316

Therefore Amount of imports of Company A in 1998 = Rs. 316 crores.