Class 7 Maths Chapter 7 Question Answers - Comparing Quantities

Q1. Mohit sold a T.V. for Rs. 3,600, gaining one-sixth of its selling price. Find the gain (in Rs.)
Ans:
Given, S.P. = Rs. 3600
Gain = 3600 / 6
= Rs. 600

Q2. 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 percentage;
Ans:
Cost price of one article = 112.50/15 = 22.5/3 = Rs. 7.5
Selling price of one article = 108/12 = Rs. 9
Profit on one article = Rs. 9 − Rs. 7.5 =  Rs. 1.5
Profit % = Profit / Cost Price x 100 = 1.5/7.5 x 100 = 20%

Q3. By selling a certain number of goods for Rs. 5,500, a shopkeeper loses equal to one-tenth of their selling price. Find the loss.
Ans:
Given, S.P.=Rs5500
Now as per given condition
Loss = 5500 / 10 = Rs. 550

Q4. A shopkeeper makes a profit of 20% on selling a transistor radio for Rs. 840. For how much should he sell another transistor radio, whose cost price is Rs. 25 more than the first one, to make the same percentage profit ?
Ans:
Case 1:
S.P of transistor = 840  Rs.
Profit = 20%
Then C.P.= 100/120 x 840 = 700 Rs.
Case 2:
C.P.of transistor = 700 + 25 = 725 Rs.
Profit = 20%
ThenS.P = 120/100 x 725 = Rs. 870

Q5. By selling tea for Rs 67.20 per kg, a profit of 12% is made, Find quantity of tea ( in kg ) bought and sold in order to gain Rs 144.
Ans:
Given,  Profit % by selling 1 kg of tea =

67.20−C.P. = 0.12C.P.
1.12C.P. = 67.20
C.P.=Rs60
Profit per kg = SP − CP = Rs67.20 − Rs60 = Rs7.20
To gain Rs144, number of kg of tea bought and sold = 144/7.20 = 20kg

Q6. State true or false:In △ABC, AD is the median and DE is parallel to BA, where E is a point in AC and hence BE is parallel to BC
A. True
B. False
Ans:

Given: AD is the median of △ABC.Hence, BD = DC.
Also, DE ∥ AB and DE is drawn from the mid point of BC, i.e. D.
Thus, by converse of mid-point theorem, DE bisects the third side, which is AC.
Then, E is the mid point of AC.
Hence, BE is the median of △ABC.
That is, the given statement is false and option B is correct.

Q7. An article marked at Rs.1000 is sold at a discount of 20%.. Find selling price of the article in Rs.
Ans: Since, Market price of an article = Rs.1000
Discount% = 20%
Discount = 1000 × 20/100 = Rs. 200
Selling price = Market price − Discount
= 1000  - 200
= Rs.800

Q8. A dealer is selling an article at a discount of 5 % on the marked price and its marked price is Rs. 140. What is the cost price, if the marked price is 12% above the cost price?
Ans:
Let the cost price be Rs. x
12% above = Rs. 1.12x
⇒ 1.12x = 140
⇒ x = 140 x 100 / 112 = Rs. 125
Therefore, the cost price of an article is Rs. 125.

Q9. A chair is bought by a trader  at 20% discount on its marked price. The marked price is Rs 7,200. If he sells it at 16% discount on its marked price, find the profit percent made in the whole transaction.
Ans:
Brought cost of chair after 20% discount = 7200 x 80 / 100 = 5760
Selling cost after 16% discount = 7200 x 84 / 100 = 6048
Profit on chair = 6048 − 5760 = 288 Rs
% of profit = 288 x 100 / 5760 = 5 %

Q10. The profit earned after selling an article for Rs. 625 is the same as loss incurred after selling the article for Rs. 435. What is the cost price of the article?
Ans:
Let the C.P. = Rs x
Then according to the question
625 − x = x−435
2x = 625 + 435
2x = 1060
x = 530
Hence C.P. of the article =Rs.530

Q11. Mohan bought 20 dining tables for Rs. 12000 and sold them at a profit equal to the selling price of 4 dining tables. The selling price of each dining table is?
Ans:
Profit = (S.P. of 20 tables) − (C.P. of 20 tables)
⇒ S.P. of 4 tables = S.P. of 20 tables − C.P. of 20 tab1es
⇒ S.P. of 16 tables = C.P. of 20 tables = Rs. 12000
⇒ S.P. of 1 dining table = Rs. 12000 / 16 = Rs. 750

Q12. If a merchant estimates his profits as 20 % of the selling price, what is his real profit percent.
Ans:
Suppose SP = Rs. 100
Profit = Rs. 20
CP = 100 − 20 = Rs. 80
Profit % = Profit / CP x 100
= 20/80 x 100
= 25%

Q13. The shopkeeper gives a discount of 12% on the pair of shoes marked for Rs. 1425, then S.P is:
Ans:
Given M.P. = Rs. 1425
Discount = 12% of Rs. 1425 = 12/100  x 1425
= Rs. 171
Selling price of shoes = Rs. (1425−171) = Rs. 1254.

Q14. A scientific calculator is available at Universal shop in Hazratganz at 20% discount and the same is available at only 15% discount at Bhootnath market. Pooja has just sufficient amount of Rs.800 to purchase it at Universal shop, Hazratganz. What is the amount that Pooja has less than the required amount to purchase it at Bhootnath?
Ans:
Let cost of calculator is Rs.10
Calculator is available at Universal shop in Hazratganj at 20% discount then sell cost =100−20=80 RS
Pooja paid Rs.800 at Universal shop
So actual cost of calculator = 800 /80 x 100 = 1000
same as 15% discount at Bhootnath market
Then selling price of calculator at bhootnath market = 85/100 x 1000 = 850 Rs.
Amount that Pooja has less paid = 850 − 800 = Rs.50

Q15. Nitesh & Jitesh invested Rs.15000 and Rs.18000 respectively in a business. If the total profit at the end of the year is Rs.8800 and Nitesh being an active partner gets an additional 12.5% of the profit. Find the total profit of Nitesh.
Ans:
Profit sharing ratio =15000:18000=5:6
Total profit =8800
Nitesh gets 12.5 % of the profit = 12.5/1000 x 8800 = Rs. 1100
Net profit = 8800 − 1100 = Rs.7700
Nitesh share in profit = 5/5 + 6 x 7700 = Rs. 3500
Total profit of Nitesh = 3500 + 1100 = Rs.4600