Question no.20 From ML aggarwal book, class10, chapter 7, ratio and proportion
In the first question we have been given ratio of pocket money of two persons also ratio of their expenditures and the amount of saving they each save. And we are asked finally the monthly pocket money.
Im second ques ratio of boys to girls is given. Their ratio get changes if we change the number of boys and girls according to question. We have to. Find the total no of students
Question 20
Solution:
(i) Consider the monthly pocket money of Ravi and Sanjeev as 5x and 7x
Their expenditure is 3y and 5y respectively.
5x – 3y = 80 …… (1)
7x – 5y = 80 …… (2)
Now multiply equation (1) by 7 and (2) by 5
Subtracting both the equations
35x – 21y = 560
35x – 25y = 400
So we get
4y = 160
y = 40
In equation (1)
5x = 80 + 3 × 40 = 200
x = 40
Here the monthly pocket money of Ravi = 5 × 40 = 200
(ii) Consider x as the number of students in class
Ratio of boys and girls = 4: 3
Number of boys = 4x/7
Number of girls = 3x/7
Based on the problem
(4x/7 + 20): (3x/7 – 12) = 2: 1
We can write it as
(4x + 140)/ 7: (3x – 84)/ 7 = 2: 1
So we get
(4x + 140)/ 7 × 7/ (3x – 84) = 2/1
(4x + 140)/ (3x – 84) = 2/1
6x – 168 = 4x + 140
6x – 4x = 140 + 168
2x = 308
x = 308/2 = 154
Therefore, 154 students were there in the class.