Percentage

  Percentage SET 02 : Q6-Q10

06. In an election between two candidates, the winning candidate has got 70% of the votes polled and has won by 15400 votes. What is the number of votes polled for loosing candidate?
1
38500
2
11550
3
26950
4
13550


Solution: 2

Let the voted poll be y

From the problems statement

⇒ 70 × y/100 - 30 × y/100 = 15400

⇒ y = (15400 × 100)/40

Votes polled for loosing party are (100 - 70)% of y

⇒ votes polled = (30 × 15400 × 100)/(100 × 40) = 11550

Alternate Method

Given:

Percentage of votes won by winning candidate = 70%

Percentage of votes obtained by losing candidate = 30%

Concept used:

Difference between the two = votes by which winning candidate won

Calculation:

40% = 15400

1% = 385

Then, votes got by losing candidate = 30% = 11550

∴ The votes polled for losing party are 11550


07. The price of a watch increases every year by 25%. If the present price is Rs. 7500, then what was the price (in Rs.) 2 years ago?
1
4800
2
5200
3
6200
4
3600

Solution: 1

Let 2 years ago the price of watch be Rs. P

1 year ago,

Price of watch = P + 25% of P = 1.25 P

This year,

Price of watch = 1.25 P + 25% of (1.25 P) = 1.5625 P

⇒ 1.5625 P = 7500

⇒ P = 4800

Let, the price before two years be P

Rate of interest (r) = 25%

Present price (A) = 7500

Time (t) = 2 years

Accordingly,

P × (1 + 25/100)2 = 7500

⇒ P × (5/4)2 = 7500

⇒ P = 7500 × (16/25)

⇒ P = 4800

∴ The price before 2 years ago was Rs. 4800.


08.The population of a town increases each year by 5% of its total at the beginning of each year. If the population on 1 January 2015 was 40000. What will it be on 1 January 2017?

1
44900
2
48400
3
44100
4
44200

Solution: 3

Concept used:

Population after T years = C.P × ((100 ± R)/100)T

Where,

C.P → Current Populations

R → Rate of change in population

T → Time 

Calculations:

Population on 1 January 2017 = 40000 × 105/100 × 105/100

⇒ 40000 × 21/20 × 21/20 = 44100

∴ Population on 1 January 2017 is 44100


09.The price of a certain item is increased by 12%. If a consumer wants to keep his expenditure on the item the same as before, how much percent must be reduce his consumption on that item?
1
15%
2

3

4


Solution: 4

The price of a certain item is increased by 12%.

Let the original price of that item be Rs. 100 per kg.

So, now the price of that item per kg = Rs. 100 × (112/100) = Rs. 112

Then, quantity of the item can be availed with Rs. 100 = 100/112 = 25/28 kg

So, quantity of item reduced by = 1 - (25/28) = 3/28 kg.

∴ The percentage of reduction in consumption = [(3/28)/1] × 100 = 
10. Arya is supposed to ride from her home to school every morning. One morning, she is in a real hurry and wishes to save 1/4th of the time. By how much percentage should she increase her speed?
1
17.56%
2
25.45%
3
33.33%
4
None of the above 

Solution: 3

Let the distance between her home and school be 100 meters

Suppose she takes x seconds normally to reach the school

Thus, normal speed = 100/x m/s

To save x/4 seconds, she should cover the same 100 meters in (x – x/4) = 3x/4 seconds

Thus, new speed = 100/(3x/4) m/s

Change in speed required = 100/(3x/4) – 100/x = 100/3x

Required percentage = (change in speed/ normal speed) × 100

⇒ % = (100/3x)/(100/x) × 100

∴ % = 33.33%

Shortcut Trick

Let the ratio between her times be = 4: 3

Time is inversely proportional to the speed so, ratio of speed = 3: 4

∴ Required speed increase = (4 - 3)/3 × 100 = 33.33%

 

 SET 01 : Q1 - Q5

 SET 05 : Q21 - Q25

SET 06 : Q26 - Q30


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