This is a basic question from ML aggarwal book of class 10th, chapter 7, ratio and proportion., ICSE board
In this ques a number in ratio a:b given and both numerator amd denominator are decreased ny a fix number then ratio becomes c:d. We have to find the number.
Question 14
Solution:
(i) Ratio = 8: 7
Consider the numbers as 8x and 7x
Using the condition
[8x – 25/2]/ [7x – 25/2] = 11/9
Taking LCM
[(16x – 25)/ 2]/ [(14x – 25)/ 2] = 11/9
By further calculation
[(16x – 25) × 2]/ [2 (14x – 25)] = 11/9
(16x – 25)/ (14x – 25) = 11/9
By cross multiplication
154x – 275 = 144x – 225
154x – 144x = 275 – 225
10x = 50
x = 50/10 = 5
So the numbers are
8x = 8 × 5 = 40
7x = 7 × 5 = 35
(ii) Consider the present income = 10x
Increased income = 11x
So the increase per month = 11x – 10x = x
Here x = Rs 600
New income = 11x = 11 × 600 = Rs 6600