# Verbal Reasoning - Arithmetic Reasoning - Discussion

Discussion Forum : Arithmetic Reasoning - Section 1 (Q.No. 2)

2.

Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A ?

Answer: Option

Explanation:

Let Rs. x be the fare of city B from city A and Rs. y be the fare of city C from city A.

Then, 2x + 3y = 77 ...(i) and

3x + 2y = 73 ...(ii)

Multiplying (i) by 3 and (ii) by 2 and subtracting, we get: 5y = 85 or y = 17.

Putting y = 17 in (i), we get: x = 13.

Discussion:

47 comments Page 1 of 5.
Raviraushan Kumar said:
11 months ago

I can't understand this, Anyone, Please, explain me to get it.

Tobiyo Kageyama said:
1 year ago

Thanks all for the explanations.

Jennie said:
3 years ago

Why should we multiply the first equation and the second equation with 3and 2? please explain.

Prince thakur said:
4 years ago

Here:

Ticket from city A and b = 2 or 2x.

Ticket from city A to C= 3 or 3x.

All cost is;

2x+3y = 77 ----> equation 1

Similarly

Ticket from city A and b = 3 or 3x

Ticket from city A to C= 2 or 2x

All cost is;

3x+2y = 73 ----> equation 2.

Now,

Cross multiply 1 and 2 equation.

We get

146x +219y=231x +154y

219y-154y=231x-146x

65y=85x.

65/85=x/y.

65 and 85 divide by 5 we get.

13/17=x/y.

Here

X=13.

Y=17.

Ticket from city A and b = 2 or 2x.

Ticket from city A to C= 3 or 3x.

All cost is;

2x+3y = 77 ----> equation 1

Similarly

Ticket from city A and b = 3 or 3x

Ticket from city A to C= 2 or 2x

All cost is;

3x+2y = 73 ----> equation 2.

Now,

Cross multiply 1 and 2 equation.

We get

146x +219y=231x +154y

219y-154y=231x-146x

65y=85x.

65/85=x/y.

65 and 85 divide by 5 we get.

13/17=x/y.

Here

X=13.

Y=17.

(4)

Gajjela said:
5 years ago

@All.

According to me, the shortcut method is;

Let Rs. x be the fare of city B from city A and Rs. y be the fare of city C from city A. And also let Rs. z be the fare for 2tickets from A to B and 2tickets from A to C.

then; z+y=77 and z+x=73,

results y-x=5.

x=13 and y=17 only satisfies the equation.

So, the answer is an option [B].

According to me, the shortcut method is;

Let Rs. x be the fare of city B from city A and Rs. y be the fare of city C from city A. And also let Rs. z be the fare for 2tickets from A to B and 2tickets from A to C.

then; z+y=77 and z+x=73,

results y-x=5.

x=13 and y=17 only satisfies the equation.

So, the answer is an option [B].

(1)

Vanshika said:
5 years ago

I can't understand is why the 1st equation is multiplied by 3 and 2nd by 2.

Vanshika said:
5 years ago

How do we get to know that 1st equation will be multiplied 3 and second by 2?

Sunil gampa said:
6 years ago

Please explain clearly how to take x y values in an equation?

Chandini said:
6 years ago

2A+3B=77.....(1)

3A+2B=73.....(2)

FROM 1&2 we get A=30-B

put A value in 1 then we get 2(30-B)+3B=77.

Finally, we get B=17.

put B value either1 or 2 eqn,

we A=13

final answer 13, 17.

3A+2B=73.....(2)

FROM 1&2 we get A=30-B

put A value in 1 then we get 2(30-B)+3B=77.

Finally, we get B=17.

put B value either1 or 2 eqn,

we A=13

final answer 13, 17.

Umar said:
6 years ago

2x+3y=77-->(1)

3x+2y=73-->(2)

73(2x+3y)=77(3x+2y),

146x+219y=231x+154y,

65y=85x,

13y=17x.

3x+2y=73-->(2)

73(2x+3y)=77(3x+2y),

146x+219y=231x+154y,

65y=85x,

13y=17x.

(2)

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