Question

Topic:- CROSS MULTIPLICATION METHOD

Q3. From a bus stand in Delhi, if we buy 2 tickets to Pitampura and 3 tickets to Dilshad Garden, the total cost is Rs 46 but if we buy 3 tickets to Pitampura and 5 tickets to Dilshad Garden, the total cost is Rs 74. Find the fares from the bus stand to Pitampura and to Dilshad Garden. Form a pair of linear equations from above data and solve it by cross- multiplication method. Also, verify the solution.

Standard:- 10

Content Quality Answer Required

No Spamming

Answer 1

Heya!

Here is yr answer.....

T = ticket (s)

Suppose, the price of T frm delhi to pitampura is x

The price of the T to dilshad garden is y

The price of the 2T from delhi to pitampura and 3T to dilshad garden = 46

2x + 3y = 46

2x + 3y - 46 = 0 ------(1)

The price of 3 T to pitampura and 5 T to dilshad garden = 74

3x + 5y = 74

3x + 5y - 74 = 0 ------(2)

Cross multiplication of (1) & (2)

2x + 3y - 46 = 0

3x + 5y - 74 = 0

$\frac{x}{3 \times ( - 74) - 5 \times ( - 46)} = \frac{y}{3 \times ( - 46) - 2 \times ( - 74)} = \frac{1}{2 \times 5 - 3 \times 3} \\ \\ \frac{x}{ - 222 + 230} = \frac{y}{148 - 138} = \frac{1}{10 - 9} \\ \\ \frac{x}{8} = \frac{y}{10} = \frac{1}{1} \\ \\ \\ now.... \\ \\ \frac{x}{8} = \frac{1}{1} \\ \\ x = 8 \\ \\ and.... \\ \\ \frac{y}{10} = \frac{1}{1} \\ \\ y = 10$

Price of T to pitampura = 8

Price of T to dilshad garden = 10

________________________

2(8)+3(10) = 46

16 + 30 = 46

46 = 46

LHS = RHS

__________________________

3(8) + 5(10) = 74

24 + 50 = 74

74 =74

LHS = RHS

__________________________



Hope it hlpz...

Answer 2

let
2X+3Y=46---1 st equation
3X+5Y=74---2 nd equation

(1st equation)-(2nd equation)

1st equation × 5 = 10X+15Y=230
2nd equation×3 = 9X+15Y=222
--------------------------------------------
X= 8
1. The cost of one ticket from bus stand to Pitampura is Rs=8

then substitute X=8 in 1st equation

2×8+3Y=46
16+3Y=46
3Y=46-16
3Y=30
Y=30/3
Y=10

2.The cost of one ticket from bus stand to Dilshad Garden is Rs=10

Now check your answer
2×8+10×3=46

3×8+10×5=74

now the answer is also cross checked