A typist charges ₹ 145 for typing 10 English and 3 Hindi pages, while charges for typing 3 English and 10 Hindi pages are ₹ 180. Using matrices, find the charges of typing one English and one Hindi page separately. However, typist charged only ₹ 2 per page from a poor student Shyam for 5 Hindi pages. How much less charged from this poor boy? Which values are reflected in this problem?

Let the cost of typing 1 English page be x.

The cost of typing 1 Hindi page is y.

Then 10x + 3y = 145... (1) × 10

3x + 10y = 180. ... (2) × 3

from 1 and 2 we get

100x + 30y = 1450

9x + 30y = 540

- - -

by solving we get

91x = 910

× = 910/91

× = 10

(1) 10x + 3y = 145

10 (10) + 3y = 145

3y = 145 - 100 = 45

y = 45/3 = 15

So x = 10 and y = 15.

Actual Rate = 15 × 5 = 75

Amount taken from shyam = 2 × 5 = 10

∴ Difference = 75 - 10 = 65

He charged 65 less to shyam

Humanity and helping poor people is reflected here.