Unitary Method

The Unitary Method is a fundamental technique used to solve problems where the value of a certain number of items is given, and we need to find the value of a different number of items. It relies on the principle of first finding the value of a single unit.

1. The Two-Step Process

To solve any problem using the unitary method, follow these two logical steps:

• Step 1: Find the value of one unit.Divide the total value by the number of items.

Step 2: Find the value of the required number of units.

Multiply the value of one item (found in Step 1) by the number of items you need to calculate.

{Total Value} = {Value of 1 item} * {Required Number of Items}

2. Direct Variation

The unitary method is most commonly applied in situations involving Direct Variation, where an increase in the number of items leads to a proportional increase in the total cost/value.

Cost of 8 pens = 10 * 8 = ₹80.

Example: If 5 pens cost ₹50, how much do 8 pens cost?

Cost of 1 pen = 50 / 5 = ₹10.

EXERCISE 13(A)

Question 1.
The price of 25 identical articles is ₹ 1,750. Find the price of :
(i) one article
(ii) 13 articles

Solution :

Question 2.
A motorbike travels 330 km in 5 litres of petrol. How much distance will it cover in :
(i) one litre of petrol?
(ii) 2.5 litres of petrol?

Solution :

Question 3.
If the cost of a dozen soaps is ₹ 460.80, what will the cost of:
(i) each soap ?
(ii) 15 soaps ?
(iii) 3 dozen soaps ?

Solution :

Question 4.
The cost of 35 envelops is ₹ 105. How many envelops can be bought for ₹ 90?

Solution :

Question 5.
If the cost of 8 cans of juice is ₹ 280, then what will be the cost of 6 cans of juice?

Solution :

Cost of 8 cans of juice = ₹ 280

Question 6.
For ₹ 378, 9 cans of juice can be bought, then how many cans of juice can be bought for ₹ 504?

Solution :

Question 7.
A motorbike travels 425 km in 5 hours. How much distance will be covered by it in 3.2 hours?

Solution :

Question 8.
If the cost of a dozen identical articles is ₹ 672, what will be the cost of 18 such articles?

Solution :

Question 9.
A car covers a distance of 180 km in 5 hours.
(i) How much distance will the car cover in 3 hours with the same speed?
(ii) How much time will the car take to cover 54 km with the same speed?

Solution :

Question 10.
If it has rained 276 cm in the last 3 days, how many cm of rain will fall in one week (7days) ? Assume that the rain continues to fall at the same rate.

Solution :

Question 11.
Cost of 10 kg of wheat is ₹ 180.
(i) What is the cost of 18 kg of wheat ?
(ii) What quantity of wheat can be purchased in ₹ 432 ?

Solution :

Question 12.
Rohit buys 10 pens for ₹ 150 and Manoj buys 14 pens for ₹ 168. Who got the pens cheaper?

Solution :

Question 13.
A tree 24 m high casts a shadow of 15 m. At the same time, the length of the shadow casted by some other tree is 6 m. Find the height of the tree.

Solution :

Question 14.
A loaded truck travels 18 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours?

Solution :

EXERCISE 13(B)

Question 1.
Weight of 15 books is 6 kg. What is the weight of 45 such books?

Solution :

Question 2.
A made 84 runs in 6 overs and B made 126 runs in 7 overs. Who made more runs per over?

Solution :

Question 3.
Geeta types 108 words in 6 minutes. How many words would she type in half an hour?

Solution :

Question 4.
The temperature dropped 18 degree Celsius in the last 24 days. If the rate of temperature drop remains the same, how many degrees will the temperature drop in the next 18 days?

Solution :

Question 5.
Mr. Chopra pays ₹ 12,000 as rent for 3 months. How much does he has to pay for a year if the rent per month remains same?

Solution :

Question 6.
A truck requires 108 litres of diesel for covering a distance of 1188 km. How much diesel will be required by the truck to cover a distance of 3300 km?

Solution :

Question 7.
If a deposit of ₹ 2,000 earns an interest of ₹ 500 in 3 years, how much interest would a deposit of ₹ 36,000 earn in 3 years with the same rate of simple interest?

Solution :

Question 8.
If John walks 250 steps to cover a distance of 200 metres, find the distance covered by him in 350 steps.

Solution :

Question 9.
25 metres of cloth costs ₹ 1,012.50.
(i) What will be the cost of 20 metres of cloth of the same type?
(ii) How many metres of the same kind can be bought for ₹ 1,620?

Solution :

Question 10.
In a particular week, a man works for 48 hours and earns ₹ 4,320. But in the next week he worked 6 hours less, how much has he earned in this week?

Solution :