Unit Test (Solutions): Comparing Quantities | Mathematics (Maths) Class 7 PDF Download

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Time: 1 hour M.M. 30 

Attempt all questions. 

• Question numbers 1 to 5 carry 1 mark each. 
• Question numbers 6 to 8 carry 2 marks each. 
• Question numbers  9 to 11 carry 3 marks each. 
• Question numbers 12 & 13 carry 5 marks each.

Q1: A shopkeeper prefers to sell his goods at the cost price but uses a weight of 800 gm instead of 1 kg weight. He earns a profit of: (1 mark)
(a) 2%
(b) 8%
(c) 20%
(d) 25%
Ans: (d)
Sol: Let CP of 1 gm = Rs. 1
Given: He sells 800 gm instead of 1000 gm (1 kg)
So, CP of 800 gm = 800 Rs.
SP of 800 gm = CP of 1000 gm = 1000 Rs.
Profit = 1000 - 800 = 200 Rs.
Profit % = (200/800) x 100 = 25%

Q2: Opposite of profit of Rs.250 is: (1 mark)
(a) profit of Rs.50
(b) loss of Rs.250
(c) loss of Rs.150
(d) none
Ans: (b)
Sol: Opposite of profit of Rs.250 is loss of Rs.250
Thus, Option B is correct.

Q3: Mohit sold a T.V. for Rs. 3,600, gaining one-fourth of its selling price. Find the gain (in Rs.) (1 mark)
Ans:
Given, S.P. = Rs. 3600
Gain = 3600 /4
= Rs. 900

Q4: Find the ratio of 800 g to 7 kg.
Ans: First, we will convert masses into the same units.
7 kg = 7 × 1000 g = 7000 g
Now, we will find the ratio of 800 g and 7000 g:
800 g : 7000 g = 800 / 7000
= 8 / 70 = 4 / 35
Required ratio is 4 : 35

Q5: Find 25% of 150%. (1 mark)
Sol: By using the formula, we have:
(25 / 100) × 150 = 37.5

Q6: Find (2 marks)
(a) 15% of 80
(b) 25% of 120
Ans:
(a) 15% of 80
We know,
15% = 15 / 100
(15 / 100) × 80 = (15 × 80) / 100
= 1200 / 100
= 12

(b) 25% of 120
= (25 / 100) × 120
= 1/4 × 120
= 30

Q7: A man buys a certain number of articles at a rate of 15 for Rs. 112.50 and sells them at a rate of 12 for Rs. 108. Find His gain as a percentage. (2 marks)
Ans:
Cost price of one article = 112.50 / 15 = 7.5
Selling price of one article = 108 / 12 = 9
Profit on one article = Rs. 9 - Rs. 7.5 = Rs. 1.5
Profit % = (Profit / Cost Price) × 100 = (1.5 / 7.5) × 100 = 20%

Q8: What rate gives an interest of Rs. 750 on a sum of Rs. 25000 in 4 years? (2 marks)
Ans:
Given, Interest, I = Rs. 750
Principal, P = Rs. 25000
Time, T = 4 years
We know, Interest = (Principal × Rate × Time) / 100
∴ Rate = (Interest × 100) / (Principal × Time)
= (750 × 100) / (25000 × 4)
= 75000 / 100000
= 0.75%

Q9: Anjali saves Rs. 7000 from her salary every month. If it is 4% of her salary, find her salary. (3 marks)
Ans:
Let Anjali’s salary = x Rs.
4% of Anjali’s salary = Rs. 7000
∴ 4% of x = 7000
⇒ 4 / 100 × x = 7000
⇒ x = 7000 × 100 / 4
⇒ x = 7000 × 25
⇒ x = 1,75,000
Therefore, Anjali’s salary is Rs. 1,75,000

Q10: It is given that the Population of Karnataka = 850 lakhs, and the population of Tamil Nadu = 780 lakhs.
The area of Karnataka = 2 lakh km², and the area of Tamil Nadu = 1.5 lakh km². (2+1 marks)
(a) How many people are present per km² in both these States? 
(b) Which of the above States is less populated?
Ans:
(a) From the above question, it is given that:
The population of the state Karnataka = 850 lakh
Area of the state Karnataka = 2 lakh km²
Then, the final population of the state Karnataka in a 1 km² area = (850 lakh) / (2 lakh km²)
= 425 people per km²
The population of Tamil Nadu = 780 lakh
Area of Tamil Nadu = 1.5 lakh km²
Then, the population of Tamil Nadu in 1 km² area = (780 lakh) / (1.5 lakh km²)
= 520 people per km²

(b) By comparing the two states, Karnataka was found to be the less populated state.

Q11: Out of 20,000 voters in a constituency, 75% of people voted. Find the percentage of voters who didn’t vote. Now, find out how many of them actually did not vote.   (3 marks)
Ans:
From the above question, it is given that:
Total number of voters present in the constituency = 20,000
The percentage of people that voted in the election = 75%
The percentage of people who did not vote in the election is = 100 - 75
= 25%
The total number of voters who did not vote in the election is = 25% of 20,000
= (25 / 100) × 20,000
= 0.25 × 20,000
= 5,000 voters

Therefore, five thousand voters did not vote.

Q12: Rohit sold two books at Rs 20 each. On one he gains 15% and on the other, he loses 15%. Then he made:  (5 marks)
(a) no profit no loss
(b) loss of 3%
(c) gain of 2%
(d) none of these
Ans: (b)
Sol:
On the first article, Rohit gains 15%.
If the cost price (CP) is 100, selling price will be 115 and profit will be Rs. 15.
When selling price is 115, profit is 15.
When selling price is 20, profit is = (15 / 115) × 20 = 2.61
Cost price = selling price - profit
= 20 - 2.61
= Rs. 17.39

On the second article, he loses 15%.
If the cost price (CP) is 100, selling price will be 85 and loss will be Rs. 15.
When selling price is 85, loss is 15.
When selling price is 20, loss is = (15 / 85) × 20 = 3.53
Cost price = selling price + loss
= 20 + 3.53
= Rs. 23.53

Total selling price = 20 + 20 = Rs. 40
Total cost price = 17.39 + 23.53 = Rs. 40.92
Net loss = 40.92 - 40 = Rs. 0.92
Loss percentage = (0.92 / 40.92) × 100 = 2.25%

Thus, Rohit makes a loss of approximately 3%.

Q13: When the price of mangoes is reduced by 15%, it enables a man to buy 10 more mangoes for Rs 50. Then find the reduced price per mango.   (5 marks)
Sol:
Let’s say Price per mango = x
Number of mangoes bought for Rs 50 = 50/x
Reduced price of mango = x - 15% of x
⇒ x - 0.15x = 0.85x
Number of mangoes that can be bought = 50/0.85x

As per the question,
⇒ (50/0.85x) - (50/x) = 10
⇒ 50/x - 50/0.85x = 10
⇒ (50 × 0.85 - 50) / (0.85x) = 10
⇒ (42.5 - 50) / (0.85x) = 10
⇒ -7.5 / (0.85x) = 10
⇒ -7.5 = 10 × 0.85x
⇒ x = 7.5 / (10 × 0.85)
⇒ x = 7.5 / 8.5
⇒ x = 0.882 (price of one mango)
Reduced price = 0.882 × 10 / 100 = 5 paise
Hence, the reduced price per mango will be 5 paise as 15% of Rs. 1 is 5 paise.