Question

Some Maths questions that I cannot solve:
i) In a bag there are coins of ₹ 2, ₹ 1 and ₹ 5 in the ratio 1 : 2 : 3. If there is ₹ 190 in all, then the number of ₹ 5 coins is ____.
ii) The scale of a map is 1 : 3000000 (3 with 6 zeros). What is the actual distance between the two towns if they are 3 cm apart on the map?
iii) The yield of wheat from 3 hectares is 112.5 quintals. Find the number of hectares required for a yield of 375 quintals of wheat. (Solve using both 'ratio and proportion' and 'unitary' method. )

The answers are:
i) 30
ii) 90 km
iii) 10 hectares

I have seen the answers from book. But, the problem is that I can't understand that how can I solve the questions. Please give the explanations.

Answer 1

Hi,
(1) total money having is Rs190
When we remove ratio,we should multipliy it with a variable.
Let the variable be x
therefore the no. Of coin are
Rs 2 is 1*x
Rs 1 is 2*x
Rs 5 is 3*x

Therefore total money is

(2*1*x)+(1*2*x)+(5*3*x)
=2x+2x+15x=19x

To find x
We know that total money having is 190Rs
Then,

19x=190
x=10

Number of Rs5 coin is 3x =3*10
=30



(2) we know that 1cm:3000000cm

i.e.. 1/3000000
Then if there is 3cm in the place of 1cm
We need to multiply the denominator also with 3cm

Then we will get 9000000cm

Converting cm to km is by dividing the number with 100000
i.e.., 9000000/100000 = 90km

(3) by ratio method
We can make the hectres we need to find be x
Then we can write
3:112.5::x:375

Therefore ,
112.5*x=3*375
x=1125/112.5
x=10 hectares

By unitary method,
First we should find how much yeild for 1 hectare

I.e.. 3/112.5

Then for 375
Is (3/112.5)*375 =10


Hope you will understand

Answer 2

1)  LET THE NUMBER OF COINS BE 1X ,2X ,3X RESPECTIVELY.
THEN EQUATION IS 
2X+2X+15X=190
19X=190
X=10
THEREFORE THE NUMBER OF FIVE RUPEE COINS ARE 30