Answers of Day 36: 1. 120
2. 4
1. Of two numbers, 3 times the smaller one is less than 4 times the larger one by 6. If the twice of the sum of their number is larger than their difference by 4. What are the two numbers?
Solution:
Let the numbers be x and y.
Considering, x is greater than y.
4x-3y=6 [condition 1] --------- Equation 1
2(x + y)-(x - y) = 4 [condition 2]
Condition 2 becomes,
x+3y = 4 --------Equation 2
By solving Equation 1 and 2, we get
x=2 and y= 2/3.
These are the 2 numbers.
2. A fraction becomes 1/3 when 1 is subtracted from both its numerator and denominator and it becomes 1/2 when 1 is added to both the numerator and denominator, find the fraction.
Solution:
Let the fraction be x/y.
(x - 1)/(y - 1) = 1/3 [condition 1]
3(x-1) = y-1
3x-y=2 ------------ Equation 1
(x+1)/(y+1) = 1/2
2(x+1) = y+1
2x-y= -1 ---------- Equation 2
By solving equation 1 and 2, we get
x=3 and y=7.
Hence, the fraction is 3/7.
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