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If one number is thrice the other and their sum is 60, find the numbers.
Let the numbers be x and y.
x is 3 times y
x = 3y …(1)
Sum of x and y is 60
x + y = 60 …(2)
Putting the value of x from (1) in (2), we get,
3y + y = 604y = 60
y = 15
x = 3 x 15
= 45
The required numbers are 15 and 45.
Find the fraction which becomes
when the denominator is increased by 5 and is equal to
when the numerator is diminished by 4.
Let the fraction by 
or 2x = y + 5
2x - y = 5 …(1)
When x is diminished by 4, fraction becomes 
or 3x - 12 = y
3x - y = 12 …(2)
2x - y = 5 …(1)
Subtracting (1) from (2), we get x = 7Substituting x = 7 in (1), we get,
2
7 - y = 5
- y = 5 - 14
- y = - 9
y = 9
The fraction is
.


6 years hence their ages will be (x + 6) years and (y + 6) years.
x + 6 = 3(y + 6)x + 6 = 3y + 18
x - 3y = 18 - 6x - 3y = 12 …(1)
3 years ago, their ages were (x - 3) years and (y - 3) years.x - 3 = 9(y - 3)
x - 3 = 9y - 27
y = 6
Substituting y = 6 in (1), we getx - 3
6 = 12
x = 12 + 18 = 30
The present age of the man is 30 years and the present age of his son is 6 years.


Sum of the digits = x + y
The number is = 10x + y
Sum of the digits is 7,
x + y = 7 …(1)
When the digits are reversed, the new number becomes
= 10y + xNew number increased by 3 = 4 times the original number
(10y + x) + 3 = 4 (10x + y)
or 10y + x + 3 = 40x + 4y
10y + x - 40x - 4y = -3-39x + 6y = -3
- 13x + 2y = -1 (Dividing by 3) …(2)Multiplying (1) by 2, we get,
2x + 2y = 14 …(3)Subtracting (3) from (2),
-15x = - 15
x = 1
1 + y = 7
y = 6
= 16
A boat goes 40 km down stream in 2 hours and returns in 4 hours. Find the speed of the boat in still water and the speed of the current.
Let the speed of the boat in still water = x km/h, and
The speed of the current be = y km/h.Time taken to go down stream = 2 hours
Time x Speed = Distance2(x + y) = 40
x + y = 20 (Divided by 2) …(1)Again, the speed of the boat upstream
= (x - y) km/hTime take to go up stream = 4 hours
Distance covered = 40 km
4(x - y) = 40
Adding (1) and (2), we get
x + y = 20 …(1)x - y = 10 …(2)
2x = 30
x = 15
Substituting x = 15 in (1),
15 + y = 20
y = 5
The speed of the boat in still water is 15 km/h and the speed of the current is 5 km/h.
A lady has 50 cents and $ 2 coins in her purse. She has 90 coins in all and their total value is $105. How many $ 2 coins does she have?
Let the number of 50 cents coins be x and
the number of $ 2 coins be y.
x + y = 90 …(1)
…(2)

x + y = 90 …(1)
3y = 120 Subtracting (1) from (2)
y = 40
The lady has 40 coins of $ 2. 
