Linear Equations Session 2

CAT
Concept Session 2: Linear Equations
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1

Session 1
Introduction to Linear Equations
Nature of solutions of Linear
Equations
Problem types – Age related
Problem types – digits related
Problem types – Successive
distribution
Other Problem types
Session 2
Problem types in LE in 3 variables –
Type 1
Problem types in LE in 3 variables –
Type 2
Concept: Integer solutions to LE in 2
variables
Special Equations using integer
solutions
Linear Equations 2

Linear Equations– Session 2
• Problem types in LE in 3 variables – Type 1
3

Linear Equations in 3 Variables 4

Type 1
Given 2 Linear Equations with 3
variables
To find Value of one variable
Feasibility condition The coefficients of other two
variables maintain the same
ratio in both the equations
Note: the ratio of the
coefficients of the variable for
which the value is to be found
should not maintain the same
ratio
Linear Equations in 3 Variables – Type 1 5

The cost of 2 pencils, 1 eraser and 3 pens is Rs.32.. The cost of 6
pencils, 3 erasers and 1 pens is Rs.29. The cost of 14 pencils, 7
erasers and seven pens is Rs.119. Find the cost of each pencil.
Answer: Option 4
1) 5 2) 3 3) 7 4) Cannot be determined

The cost of 2 oranges, 3 apples and 2 mangoes is Rs. 67. The cost
of 4 oranges, 6 apples and 1 mango is Rs. 89. The cost of 6
oranges, 9 apples and 3 mangoes is Rs. 156. What is the cost of an
apple?
Answer: Option 4

Rahim owns a stationery store where he buys old sharpeners and
sells pencils and erasers. On Monday he sold 4 pencils, 3 erasers
and bought 6 old sharpeners the net change in the money that he
had was an increase by Re. 1 (Assume that the only cause of
change in the money he has is the transactions involving the above
three commodities). On Tuesday he bought 27 old sharpeners and
sold 18 pencils and 16 erasers. The net change in the money was
an increase of Rs. 12. If he buys 21 old sharpeners and sells 14
pencils and 9 erasers, then what is the net change in the money he
has on Wednesday? (In Rs.)
Answer: Option 1
1) Decrease by 1 2) Increase by 5 3) Decrease by 7 4) Cannot be determined

• Problem types in LE in 3 variables –
Type 2
9

Type 2
Given 2 Linear Equations with 3
variables
To find Value of the given combination of
the three variables
Feasibility condition Existence of a unique k and l value*

If the cost of one mango, five apples and 7 bananas is Rs.84 and
cost of one mango, seven apples and 10 bananas is Rs. 114. Find
the cost of 9 mangoes, 23 apples and thirty bananas.
K= 20 L= - 11 Ans: 426
Linear Equations in 3 Variables – Type 2
11

The cost of 7 bananas, 5 apples and 3 oranges is Rs. 48. The cost
of 3 apples, 5 bananas and 4 oranges is Rs.40. What is the cost of
7 oranges, 5 apples and 3 bananas?
Answer: Option 4
Linear Equations in 3 Variables – Type 2
12

• Concept: Integer solutions for linear equations in 2
variables
13

Integer solutions for Linear Equations in 2 variables 14

• Special Equations using integer solutions
15

Kumar takes up a project where for each day of his work he is paid
Rs. 100 and on a day he takes lunch from the firm’s canteen Rs. 16
is deducted from his daily pay. If at the end of the month he is paid
Rs. 2420, then for how many days did he take lunch in the firm’s
canteen? [ Assume that he takes lunch from the firm’s canteen only
if he works on that day]
Answer: Option 2
Special Equations
16

A bookshop owner classifies all the books he has in the shop under
three categories, non-fiction, fiction and children’s books. Each non-
fiction is sold at Rs. 150, each fiction book is sold at Rs. 60 and each
children’s book is sold at Rs. 33. If the total sale on a day in the book
shop by selling books is Rs. 639 and at least one book on each of
the categories is sold, in how many different combinations could he
have sold the books?
Answer: Option 3
1) 3 2) 3 3) 2 4) None of these
Special Equations 17

A confused bank teller transposed the rupees and paise when he cashed a
cheque for Shailaja giving her rupees instead of paise and paise instead of
rupees. After buying a toffee for 50 paise, Shailaja noticed that she was left with
exactly three times as much as the amount on the cheque. Which of the
following is a valid statement about the cheque amount?
Answer: Option 4
1) Over Rupees 13 but less than Rupees 14
5) Over Rupees 4 but less than Rupees 5 CAT 2007
Special Equations 18

Linear Equations Session 2

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