Question

The taxi charges in Hyderabad are fixed, along with the charge for the distance covered.
Upto first 3 km you will be charged a certain minimum amount. From there onwards you
have to pay additionally for every kilometer travelled. For the first 10 km, the charge paid
is 166. For a journey of 15 km. the charge paid is 3256.
i What are the fixed charges and charge per km?
i How much does a person have to pay for travelling a distance of 25 km?​

Answer 1

Given :

• Upto 3 km a person is charged a certain minimum amount.
• After 3 km, person has to pay additionally for every km.
• For 1st 10 km the charge is ₹ 166.
• For a journey of 15 km, the charge paid is ₹ *256.*

To Find :

• Fixed charge
• Charge per km
• Charge to be paid for travelling 25 km.

Solution :

Let the fixed charge be ₹ x.

Let the charge per km be ₹ y.

Case 1 :

For first 10 km the charge paid is ₹166.

Equation :

$\longrightarrow$ $\sf{x+(10y-3y)=166}$

$\bold{\big[The\:charge\:for\:first\:3\:km\:is\:fixed\big]}$

$\longrightarrow$ $\sf{x+(7y) =166}$

$\longrightarrow$ $\sf{x+7y=166}$

$\longrightarrow$ $\sf{x=166-7y\:\:\:(1)}$

Case 2 :

For travelling 15 km, the charge paid is ₹ 256.

Equation :

$\longrightarrow$ $\sf{x+(15y-3y)=256}$

$\longrightarrow$ $\sf{x+(12y) =256}$

$\longrightarrow$ $\sf{x+12y=256}$

$\longrightarrow$ $\sf{166-7y+12y=256}$

$\bold{\big[From\:equation\:(1)\:=\:x\:=\:166\:-7y\big]}$

$\longrightarrow$ $\sf{166+5y=256}$

$\longrightarrow$ $\sf{5y=256-166}$

$\longrightarrow$ $\sf{5y=90}$

$\longrightarrow$ $\sf{y=\dfrac{90}{5}}$

$\longrightarrow$ $\sf{y=18}$

Substitute, y = 18 in equation (1),

$\longrightarrow$ $\sf{x+7y=166}$

$\longrightarrow$ $\sf{x+7(18)=166}$

$\longrightarrow$ $\sf{x+126=166}$

$\longrightarrow$ $\sf{x=166-126}$

$\longrightarrow$ $\sf{x=40}$

Now, charge paid for 25 km, will be fix charge plus the charge per km into distance.

$\longrightarrow$ $\sf{x+(25y-3y)}$

$\longrightarrow$ $\sf{40+22y\:\:}$

$\longrightarrow$ $\sf{40+22(18)}$

$\longrightarrow$ $\sf{40+396}$

$\longrightarrow$ $\sf{436}$

$\large{\boxed{\bold{Fixed\:Charge\:=\:x\:=\:\:Rs.\:\:40}}}$

$\large{\boxed{\bold{Charge\:per\:km\:=\:y\:=\:\:Rs.\:18}}}$

$\large{\boxed{\bold{\:Charge\:paid\:for\:journey\:of\:25\:km\:=\:Rs.\:436}}}$