Question - 12 : - The car hire charges in a city comprise of a fixed charges together with the charge for the distance covered. For a journey of 12 km, the charge paid is ₹ 89 and for a journey of 20 km, the charge paid is ₹ 145. What will a person have to pay for travelling a distance of 30 km?

Answer - 12 : -

Let the fixed charges = ₹ x

and charges per km = ₹ y

According to the given conditions

Question - 13 : - A part of monthly hostel charges in a college are fixed and the remaining depend on the number of days one has taken food in the mess. When a student A takes food for 20 days, he has to pay ₹ 1000 as hostel charges whereas a student B, who takes food for 26 days, pays ₹ 1180 as hostel charges. Find the fixed charged and the cost of food per day. [CBSE 2000]

Answer - 13 : -

Let the fixed charge of the college hostel = ₹ x

and daily charges = ₹ y

According to the given conditions,

x + 20y = 1000 …(i)

x + 26y =1180 …(ii)

Subtracting (i) from (ii), we get

6y = 180

=> y = 30

Substituting the value of y in (i)

x + 20 x 30 = 1000

=> x + 600 = 1000

=> x = 1000 – 600 = 400

Fixed charges = ₹ 400 and daily charges = ₹ 30

Question - 14 : - Half the perimeter of a garden whose length is 4 m more them its width is 36 m. Find the dimensions of the garden.

Answer - 14 : -

Let the length of the garden = x m

and width = y m

x – y = 4 …(i)

and x + y = 36 ….(ii)

Adding we get,

2x = 40

=> x = 20

and subtracting,

2y = 32

y = 16

Length of the garden = 20 m and width = 16 m

Question - 15 : - The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them

Answer - 15 : -

In two supplementary angles,

Let larger angle = x

and smaller angle = y

x – y = 18°

But x + y = 180°

Adding we get,

2x = 198°

=> x = 9°

Subtracting the get,

2y = 162°

=> y = 81°

Angles are 99° and 81°

Question - 16 : - 2 women and 5 men can together finish a piece of embroidery in 4 days while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the embroidery and that taken by 1 man alone.

Answer - 16 : -

Let one woman can do the work in = x days

and one man can do the same work = y days

Question - 17 : - Meena went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Meena got 25 notes in all. Find how many notes ₹ 50 and ₹ 100 she received.

Answer - 17 : -

Total amount with drawn = ₹ 2000

Let number of ₹ 50 notes = x

and of ₹ 100 = y

According to the conditions

x + y = 25 …(i)

and 50x + 100y = 2000

=> x + 2y = 40 ….(ii)

(Dividing by 50)

Subtracting (i) from (ii), y = 15

Substituting the value of y in (i)

x + y = 25

x + 15 = 25

=> x = 25 – 15 = 10

Number of 50 rupees notes = 10

and number of 100 rupee notes = 15

Question - 18 : - There are two examination rooms A and B. If 10 candidates are sent from A to B, the number of students in each room is same. If 20 candidates are sent from B to A, the number of students in A is double the number of students in B. Find the number of students in each room.

Answer - 18 : -

Let A examination room has students = x

and B room has students = y

According to the given conditions,

x – 10 = y + 10

=> x – y = 10 + 10

=> x – y = 20 ….(i)

and x + 20 = 2 (y – 20)

=> x + 20 = 2y – 40

=> x – 2y = – 40 – 20 = – 60 ….(ii)

Subtracting (ii) from (i), y = 80

Substituting the value of y in (i)

x – 80 = 20

=> x = 20 + 80 = 100

In examination room A, the students are = 100

and in B room = 80

Question - 19 : - A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Mumbai to Ahmedabad costs ₹ 216 and one full and one half reserved first class tickets cost ₹ 327. What is the basic first class full fare and what is the reservation charge?

Answer - 19 : -

Let the rate of fare of full ticket = ₹ x

and rate of reservation = ₹ y

According to the given conditions,

x + y = 216 …(i)

Question - 20 : - A wizard having powers of mystic in candations and magical medicines seeing a cock, fight going on, spoke privately to both the owners of cocks. To one he said; if your bird wins, than you give me your stake-money, but if you do not win, I shall give you two third of that. Going to the other, he promised in the same way to give three fourths. From both of them his gain would be only 12 gold coins. Find the stake of money each of the cock- owners have.

Answer - 20 : -

Let the first owner of cock has state money = x gold coins

and second owner has = y gold coins

According to the given conditions,

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