1. In the Science City, Kolkata the rate of the ticket is increased by 50% to increased the revenue but simultaneously 20% of the visitor decreased. What is percentage change in the revenue. if it is known that the Science city collects one revenue only from the visitors and it has no other financial supports:

a) +20%

b) -25%

c) +30%

d) -30%

Explanation: Let the initial revenue be 100

100 === 50% ↑ (Ticket up) ===> 150 === 20% ↓ (Visitors down) ===> 120

There is 20% increase in the revenue

2. Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?

a) 57%

b) 60%

c) 65%

d) 90%

Explanain : Total number of votes polled

= (1136 + 7636 + 11628)

= 20400

Required percentage

= $$\left( {\frac{{11628}}{{20400}} \times 100} \right)\% $$

= $$57\% $$

3. An alloy contains the copper and aluminum in the ratio of 7 : 4 While making the weapons from this alloy, 12% of the alloy got destroyed. If there is 12 kg of aluminum in the weapon, then weight of the alloy required is :

a) 14.4 kg

b) 37.5 kg

c) 40 kg

d) 48 kg

Explanation: Copper : Aluminum = 7 : 4

Let Copper and Aluminum in the weapon be 7x and 4x respectively

Given, Aluminum in weapon = 12 kg

So, 4x = 12

x = 3

Copper = 7x = 7 × 3 = 21 Kg.

Total alloy in the weapon = 12 + 21 = 33 kg

But 12% alloy get destroyed in making the weapon, i.e. 88% alloy is used in the weapon,

88 % alloy = 33 kg

100 % alloy = 37.5 kg

4. 80% of a smaller number is 4 less than 40% of a larger number. The larger number is 85 greater than the smaller one. The sum of these two number is

a) 325

b) 425

c) 235

d) 500

Explanation: Let the smaller number be x and larger number be y

According to the question,

80% of x + 4 = 40% of y

4y - 8x = 40

y - 2x = 10 ----- (1)

y - x = 85 ----- (2)

By using (1) and (2),

x = 75

y = 160

x + y = 235

5. A number x is mistakenly divided by 10 instead of being multiplied by 10. what is the percentage error in the result?

a) -99%

b) -100%

c) +99%

d) +100%

Explanation: Actual result = 10x

By mistake it has been divided by 10 = $$\frac{x}{{10}}$$

%Change = $$ {\frac{{10x - \left( {\frac{{10}}{x}} \right)}}{{10x}}} $$ × 100 = 99 = -99%

Since, actual value is greater than the wrong value.

6. Out of the total production of iron from hematite, an ore of Iron, 20% of the ore gets wasted, and out of the remaining iron, only 25% is pure iron. If the pure iron obtained in a year from a mine of hematite was 80,000 kg, then the quantity of hematite mined from that mine in the year is

a) 5,00,000 kg

b) 4,00,000 kg

c) 4,50,000 kg

d) None of these

Explanation: Let 100 kg of hematite be obtained then 20% of it get wasted that means 80 kg of ore remains.

Pure iron = 25% of remaining ore = $$\frac{{80 \times 25}}{{100}} = 20\,{\text{kg}}$$

20 kg pure Iron is obtained from 100 of hematite

1 kg pure Iron is obtained from = $$\frac{{100}}{{20}}$$ hematite

80000 kg pure Iron is obtained from =$$\,\frac{{100}}{{20}} \times 80000 = \,$$ $$400000\,{\text{kg}}$$ hematite.

7. A man buys a truck for Rs. 2,50,000. The annual repair cost comes to 2% of the price of purchase. Besides, he has to pay an annual tax of Rs. 2000. At what monthly rent must he rent out the truck to get a return of 15% on his net invests of the first year?

a) Rs. 3359

b) Rs. 2500

c) Rs. 4000

d) Rs. 3212.5

Explanation: The total cost for the year

= 250000 + 2% of 2500000 + 2000

= Rs. 257000

For getting return of 15% he must earn

= $$\frac{{257000 \times 15}}{{100}}$$

= Rs. 38550 per year

Monthly Rent = $$\frac{{38550}}{{12}}$$

= Rs. 3212.5

8. Ram spends 30% of his salary on house rent, 30% of the rest he spends on his children's education and 24% of the total salary he spends on clothes. After his expenditure, he is left with Rs. 2500. What is Ram's salary?

a) Rs. 11,494.25

b) Rs. 20,000

c) Rs. 10,000

d) Rs. 15,000

Explanation: Let Ram's salary be x

He spends on rent = 30% of x = $$\frac{{30{\text{x}}}}{{100}}$$

He spends on education = 30% from rest of the salary = $$\frac{{30 \times 70{\text{x}}}}{{100 \times 100}} = \frac{{21{\text{x}}}}{{100}}$$

He Spends on clothes = 24% of total salary = $$\frac{{24{\text{x}}}}{{100}}$$

Saving = 2500

Salary of ram = x

$$\eqalign{ & \frac{{30{\text{x}}}}{{100}} + \frac{{21{\text{x}}}}{{100}} + \frac{{24{\text{x}}}}{{100}} + 2500 = {\text{x}} \cr & \frac{{75x}}{{100}} = {\text{x}} - 2500 \cr & 75{\text{x}} = 100{\text{x}} - 250000 \cr & 100{\text{x}} - 75{\text{x}} = 250000 \cr & {\text{x}} = \frac{{250000}}{{25}} \cr & {\text{x}} = 10000 \cr & {\text{Ram's}}\,{\text{salary = Rs}}{\text{.}}\,10000 \cr} $$

9. A report consists of 20 sheets each of 55 lines and each such line consist of 65 characters. This report is reduced onto sheets each of 65 lines such that each line consists of 70 characters. The percentage reduction in number of sheets is closer to

a) 20%

b) 5% more

c) 30% less

d) 35% less

Explanation: Let x be the page required when report is retyped

Now, we can use work equivalence method

20 × 55 × 65 = 70 × 65 × x

x = $$\frac{{20 \times 55 \times 65}}{{70 \times 65}}$$

x = 15.70 = 16 pages.

% reduction in pages = $$\left( {20 - 16} \right) \times \frac{{100}}{{20}}$$ $$\, = \,$$ $$20\% $$

10. The price of Maruti car rises by 30 percent while the sales of the car come down by 20%. What is the percentage change in the total revenue?

a) - 4%

b) - 2%

c) + 4%

d) + 2%

Explanation: 100 == 30%↑(price effect) ==> 130 == 20%↓(sales effects) ==> 104

Hence, 4% rises