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Published on: 18/09/2019
Comparing Quantities
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1.
Shankar bought a second hand refrigerator for Rs 2500. He spent Rs 500 on its repairs and sold for Rs 3300. Find his loss or gain per cent.
2.
The list price of a frock is Rs 220. A discount of 20% is announced on it. What is the amount of discount on it and its sale price?
3.
An item marked at Rs 840 is sold for Rs 714. What is the discount and discount %?
4.
Rahul got 150 marks out of 200 and Prabha got 180 marks out of 300. Whose performance is better?
5.
A picnic is being planned in a school for class VIII. Girls are 60% of the total number of students and are 18 in number.
If the picnic spot is 55 km from the school and their first stop is at 22 km from the school, what per cent of the total distance is this?
6.
A picnic is being planned in a school for class VIII. Girls are 60% of the total number of students and are 18 in number.
What is the ratio of the number of boys to the number of girls?
7.
A computer monitor is marked at Rs 15600 and it is available for Rs 12480. Find the discount given and discount percent.
8.
The cost of a calculator is Rs 750. The sales tax is charged 5%. Find the bill amount.
9.
A shirt is marked at Rs 850 and is sold for Rs 765. What is the discount and discount percent?
10.
Anirudha bought 100 pencils at the rate of Rs 3.50 per pencil and pays a sales tax of 4%. Find the total amount paid by Anirudha.
11.
Ankit buys a memory card costing Rs 550. If the rateof sales tax is 5%, then find the total amount payable by him.
12.
If \(\frac{7}{3}\) % of a number is 147, then find the number.
13.
Find the time period and rate tor each a sum taken for 1\(\frac{1}{2}\)yr at 8% per annum is compounded half-yearly.
14.
Find the population of a city after 3 yr, which is at present 12lakh, if the rate of increase is 3%.
15.
Find the time period and rate for which a sum taken for 3 yr at 6% per annum is compounded half-yearly.
1.
Profit = 10%
2.
Marked price is same as the list price.
20% discount means that on RS. 100 (MP), the discount is RS. 20.
By unitary method, on RS.1 the discount will be RS. \(\frac{20}{100}\)
On RS. 220, discount = RS. \(\frac{20}{100} \times 220=\ Rs. 44\)
The sale price = (RS. 220 – RS. 44) or RS. 176
Rehana found the sale price like this —
A discount of 20% means for a MP of RS. 100, discount is RS. 20. Hence the sale price is RS. 80. Using unitary method, when MP is RS. 100, sale price is RS. 80;
When MP is RS. 1, sale price is RS.\(\frac{80}{100}\)
Hence when MP is RS. 220, sale price = RS. \(\frac{80}{100} \times 220=\text { RS. } 176\)
3.
Discount = Marked Price – Sale Price
= RS. 840 – RS. 714
= RS. 126
Since discount is on marked price, we will have to use marked price as the base.
On marked price of RS. 840, the discount is RS. 126.
\(\text { Discount }=\frac{126}{840} \times 100 \%=15 \%\)
4.
Rahul
5.
40%
6.
2:3
7.
Marked price of the monitor = Rs 15600
Sales price of the monitor = Rs 12480
\(\therefore\)Discount = [Marked price] - [Sales price]
= Rs 15600 - Rs 12480 = Rs3120
\(\therefore\)Discount per cent = \(3120\over 15600\)x 100% = 20%
8.
The price of the calculator = Rs 750
Sales tax = 5% of Rs750
\(=Rs {5\over100}\times 750=Rs{75\over2}=Rs37.5\)
\(\therefore\)Bill amount = Sales Price + Sales Tax
=Rs 750 + Rs 37.5 = Rs 787.5
9.
Marked price of the shirt = Rs 850
Selling price of the shirt = Rs 765
\(\therefore\) Discount = [Marked price] - [Selling price]
= Rs 850 - Rs 765 = Rs 85
Now, d.iscount per cent =\({85\over 850}\times 100\%=10\%\)
10.
Rs 364
11.
Total amount payable by Ankit
= 550 + 5% of cost price
= 550 + \(\frac{5}{100}\times 550\)
= \(550+\frac{55}{2}=\frac{1100+55}{2}\) = Rs 577.5
12.
∵ \(\frac{7}{3}\)% of the number = 147
⇒ \(\frac{7}{300}\)xNumber = 147
∴ Number = 147x\(\frac{300}{7}\)= 6300
13.
Here, time period (T) = 1\(\frac{1}{2}\)yr = \(\frac{3}{2}\)yr and rate = 8%
For half-yearly, time period, T =\(\frac{3}{2}\)x2 = 3
and rate = \(\frac{8}{2}\)% = 4 %
14.
Given, P = Rs 1200000, R = 3% per annum and n =3 yr
∴ A = P\((1+\frac{R}{100})^{n}\)= 1200000\((1+\frac{3}{100})^{3}\)=1200000\((\frac{103}{100})^{3}\)= 1200000x\((\frac{103}{100})\)x\((\frac{103}{100})\)x\((\frac{103}{100})\)
= 1311272 (approx).
Hence, the population of the city will be 1311272 after three years.
15.
Here, time period (T) = 3 yr and rate = 6% for half-yearly
∴ Time period (T) = 3 x 2 = 6 and rate =\(\frac{6}{2}\)% = 3%
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