Q4 of 23 Page 1

Attempt any two sub-questions from the following:

Solve the following simultaneous equations: 27/(x-2) + 31/(y+3) = 85; 31/(x-2) + 27/(y+3) = 89.

Given equations are 27/(x-2) + 31/(y+3) = 85; 31/(x-2) + 27/(y+3) = 89.

Let 1/(x-2) = a and 1/(y+3) = b


Given equations becomes


27a + 31b = 85 ………………..(1)


31a + 27b = 89 ………………..(2)


Adding (1) and (2)


27a + 31b + 31a + 27b = 85 + 89


⇒ 58a + 58b = 174


⇒ 58 (a + b) = 174


⇒ a + b = 3 …………………(3)


Subtracting equation (1) and (2)


27a + 31b – 31a – 27b = 89


⇒ -4a + 4b = -4


⇒ a – b = 1 …………………(4)


Adding equation (3) and (4)


a + b + a – b = 4


⇒ 2a = 4


⇒ a = 4/2


⇒ a = 2


Putting value of a in (4)


2 – b = 1


⇒ b = 2 – 1


⇒ b = 1


Resubstituting


a = 1/(x – 2)


⇒ 1/(x – 2) = 2


⇒ 1 = 2x – 4


⇒ 2x = 1 + 4


⇒ x = 5/2


b = 1/(y + 3)


⇒ 1 = 1/(y + 3)


⇒ y + 3 = 1


⇒ y = 1 – 3


⇒ y = -2


∴ x = 5/2 and y = -2


More from this chapter

All 23 →
3

Attempt any three sub-question from the following:

The number of hours, spent by a school boy in different activities in a day is given below:



Present the above information using pie diagram.

 4

Attempt any two sub-questions from the following:

Babubhai borrows 4,000 and agrees to repay with a total interest of 500 in 10 instalments, each instalment being less than the preceding instalment by 10, should be the first and last instalments?

 4

Attempt any two sub-questions from the following:

Two dice are thrown, find the probability of getting:
(a) The sum of the numbers on their upper faces is at least 10.
(b) The sum of the number on their upper faces kin divisible by 5.
(c) The number on the upper face of the first die is greater than the number on the upper face of the second die.

 5

Attempt any two sub-questions from the following:

When the son will be as old as his father today, the sum of their ages then will be 126 years. When the father was as old his son is today. The sum of their ages then was 38 years. Find their present ages.