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QUESTION: 1

Find the ratio of 5 m to 10 km.

Solution:

5:10

covert 10km to meter

1km=1000m

10km= 10000m

so,

5:10000= 5/10000

= 1/2000 =1:2000

QUESTION: 2

An item marked at Rs 840 is sold for Rs 714. What is the discount %?

Solution:

Given, marked price = 840

selling price = 714

We know that Discount = MP - SP

= 840 - 714

= 126.

Discount% = 126/840 * 100

= 15%.

QUESTION: 3

Find selling price (SP) if a profit of 5% is made on a cycle of Rs 700 with Rs 50 as overhead charges.

Solution:

Total Cost = 700+50 = 750

Profit = 5% of 750 = 37.5

SP = CP+P = 750+37.5 = 787.5

QUESTION: 4

Find the ratio of speed of a cycle 20 km per hour to the speed of scooter 30 km per hour.

Solution:

20 : 30 or 20/30

= 2 : 3 or 2/3

QUESTION: 5

Find the ratio of speed of a car 50 km per hour to the speed of scooter 40 km per hour.

Solution:

50 : 40 or 50/40

= 5 : 4 or 5/4

QUESTION: 6

Find the ratio of speed of a train 120 km per hour to the speed of car 90 km per hour.

Solution:

120 : 90 or 120/90

= 4 : 3 or 4/3

QUESTION: 7

The price of a car was Rs 3,40,000 last year. It has increased by 20% this year. What is the price now?

Solution:

Original price = 3,40,000

20% increase = 20/100 * 3,40000

= 68000

New price = 3,40,000 + 68000

= 4,08,000

QUESTION: 8

The price of a motor bike was Rs 60,000 last year. It has increased by 15% this year. What is the price now?

Solution:

As it was 60,000 initially, but now there is an increase of 15%.

so we calculate 15% of 60,000 that will be ₹9,000.

Then we have to calculate the new price of bike, (i.e. old + increased) = ₹60,000+₹9,000 = ₹69,000

QUESTION: 9

The price of a house was Rs 34,000 last year. It has increased by 20% this year. What is the price now?

Solution:

QUESTION: 10

The price of a car was Rs 5,00,000 last year. It has increased by 10% this year. What is the price now?

Solution:

As it was 5,00,000 initially, but now there is an increase of 10%.

so we calculate 10% of 5,00,000 that will be ₹50,000.

Then we have to calculate the new price of bike, (i.e. old + increased) = ₹5,00,000+₹50,000 = ₹5,50,000

QUESTION: 11

Rohit bought a machine for Rs 20,000, then spent Rs 500 on its repairs and sold it for Rs 30,000. Find his loss or gain per cent.

Solution:

Cost price of washing machine = 20,000 + 5,00

= 20,500 Rs.

Selling price = Rs. 30,000

Gain = S.P. - C.P. = 30,000 - 20,500

9,500 Rs.

Therefore, Gain percent = (Gain * 100)/ C.P.

= (9,500 * 100)/ 20,500

= 46%

QUESTION: 12

Sohan bought a washing machine for Rs 40,000, then spent Rs 5,000 on its repairs and sold it for Rs 50,000. Find his loss or gain per cent.

Solution:

Cost price of washing machine = 40,000 + 5,000

= 45,000 Rs.

Selling price = Rs. 50,000

Gain = S.P. - C.P. = 50,000 - 45,000

5,000 Rs.

Therefore, Gain percent = (Gain * 100)/ C.P.

= (5,000 * 100)/ 45,000

= 11%

QUESTION: 13

A picnic is being planned in a school for Class VI. Girls are 40% of the total number of students and are 20 in number. Find the ratio of the number of girls to the number of boys in the class.

Solution:

Let the total no. of students be x.

No. of girls= 20

No. of boys = x-20

A. T. Q. ,

40% of x= 20

=> 40/100 × x = 20

=> x= 20× 100/40

=> x= 50

So, total no. of students = 50

No. of girls= 20

No. of boys = 50-20 = 30

Ratio of girls to boys = 20:30

= 20/30

=2/3

=2:3

QUESTION: 14

A picnic is being planned in a school. Girls are 60% of the total number of students and are 18 in number. Find the ratio of the number of girls to the number of boys in the class.

Solution:

Girls are 60% of the total number of students and are 18 in number.

Let say total students = T

Girls = (60/100)T

=> 18 = 3T/5

=> T = 30

Boys = 30 - 18 = 12

Ratio of Girls to boys = 18 : 12

=> 3 : 2

QUESTION: 15

A shopkeeper purchased 300 bulbs for Rs 10 each. However 10 bulbs were fused and had to be thrown away. The remaining were sold at Rs 12 each. Find the gain or loss %.

Solution:

Shopkeeper purchased 300 bulbs for ₹3000

If 10 bulbs were fused, the cost of 10 bulbs is ₹100

If he sell 290 bulbs as ₹12 each = 290×12 =3480

when he sell the the cost of each bulb as ₹12 he got ₹480 profit

As a percentage = 480÷3000×100=16

so he got 16% profit

QUESTION: 16

A shopkeeper purchased 500 pieces for Rs 20 each. However 50 pieces were spoiled in the way and had to be thrown away. The remaining were sold at Rs 25 each. Find the gain or loss %.

Solution:

Number of pieces = 500

Cost per piece = 20

Therefore, total cost price = 500 * 20 = 10000

Number of spoiled pieces = 50

Then, number of pieces sold = 500 - 50 = 450

Selling price of each piece = 25

Therefore, total selling price = 450 * 25 = 11250

Since SP>CP, therefore it's a gain.

Gain % = [(SP - CP)/CP] * 100

= [(11250 - 10000)/10000] * 100

= (1250/10000) * 100

= 12.5 %

QUESTION: 17

During a sale, a shop offered a discount of 20% on the marked prices of all the items. What would a customer have to pay for a pair of jeans marked at Rs 1450 and a shirt marked at Rs 850 each?

Solution:

Discount on Jeans=20% of 1450=290

Price of jeans=1450-290=1160

Discount on shirt=20% of 850=170

Price of shirt=850-170=680

Total price=1160+680= 1840

QUESTION: 18

During a sale, a shop offered a discount of 10% on the marked prices of all the items. What would a customer have to pay for a pair of jeans marked at Rs 1450 and two shirts marked at Rs 850 each?

Solution:

Given: MP (marked price) of 1 pair of jeans=₹1450

MP of 1 shirt= ₹850

Total Marked Price (MP) of a pair of jeans and two shirts

= 1450 + 2 x 850 = 3150

Total MP= ₹3150

Discount = Marked Price (MP) x % Discount

=3150 × (10/100)= ₹315

New Price After Discount = 3150 - 315 =₹ 2835

A customer would have to pay for a pair of jeans and two shirts =₹2835

QUESTION: 19

The population of a city was 30,000 in the year 2011. It increased at the rate of 5% p.a. Find the population at the end of the year 2013.

Solution:

Population of the city in 2011 = 30,000

Percentage increased = 5%

Therefore 5% of 30,000 = 5/100 × 30,000 = 1,500

Population increased in 2 years = 1,500 × 2 = 3,000

Therefore population in 2013 = 30,000 + 3,000 = 33,000

QUESTION: 20

The population of a city was 40,000 in the year 1999. It increased at the rate of 10% p.a. Find the population at the end of the year 2000.

Solution:

Population of the city in 1999 = 40,000 Percentage increased = 10% Therefore 10% of 40,000 = 10/100 × 40,000 = 4,000 Population of the city in 2000 = 40,000 + 4,000 = 44,000

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