Question 196884: 1.Find the two numbers whose sum is 108 and whose difference is 24.
2. The cost of 5 tables is the same as the cost of 8 chairs. If the cost of 4 tables and 9 chairs is 3080 Rs. Find the cost of each.
3. Five years ago, A's age was four times B's age, 6 years hence A's age to B's age is 5:2. Find the ages of A and B at present.
4. If the length of a rectangular room is decreased by 2m and its breadth increased by 5m, its area would increase by 80 sq.m. If the length is increased by 3 m and its breadth decreased by 2m, its area would decrease by 20 sq.m. Find the length and breadth of the room.
Answer by J2R2R(94)   (Show Source):
You can put this solution on YOUR website! 1.
Let x be the bigger number and y the smaller number
x + y = 108; x - y = 24
This gives 2x = 132; x = 66 therefore y = 42
2.
Let c be the price of a chair and t be the price of a table
5t = 8c; 4t + 9c = 3080
Substitute 5t/8 for c: 4t + 45t/8 = 3080; 77t/8 = 3080; 77t = 24640; t = 320 and c = 200
A table costs 320 Rs and a chair costs 200 Rs.
3.
Let A’s age be a, and B’s age be b.
From the information given, we have for five years ago; a - 5 = 4(b - 5) which gives
a - 5 - 4b + 20 = 0; a - 4b = - 15
6 years hence (which is one year on from now); (a + 1):(b + 1) = 5:2; 2(a + 1) = 5(b + 1) which gives
2a + 2 = 5b + 5; 2a - 5b = 3
If a - 4b = - 15 we have 2a - 8b = - 30
This combined with 2a - 5b = 3 gives 3b = 33; b = 11; a = 29
Therefore the age for A is 29 years and B is 11 years.
4.
Let the lengths be l and the breadth be b
(l - 2)(b + 5) = lb + 80 giving lb + 5l - 2b - 10 = lb + 80; 5l - 2b = 90 giving 15l - 6b = 270
(l + 3)(b - 2) = lb - 20 giving lb - 2l + 3b - 6 = lb - 20; - 2l + 3b = - 14 giving - 4l + 6b = - 28
Add these last two gives: 11l = 242; therefore l = 22; b = 10
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