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CDS Exam ELEMENTARY MATHEMATICS Study Material

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Percentage Discount

If Ram got 30% marks and failed by 15 marks and Mohan got 40% and scored 35 more than pass marks. What is percentage necessary for passing ?

a) 40%
b) 38%
c) 33%
d) 43%

✔Answer

✔Solution

Correct Answer Is : 33%

Solution Is : Let maximum marks be x, then Given, Ram got pass marks = 30% of x + 15 = x * 30/100 + 15 Mohan got pass marks =x * 40/100 - 35 According to question, 3x + 150 = 4x - 350 x = 150 + 350 = 500 pass marks = 500 * 3/10 + 15 = 165 Necessary percentage for passing = 165/500 * 100 = 33%.

5 kg of tea and 8 kg of sugar together cost 172 ₹. The price of tea has risen by 20% and that of sugar by 10%. Hence the same quantities of tea and sugar now cost 199.20 ₹ . What is the original price of tea per kg ?

a) 18 per kg
b) 19 per kg
c) 20 per kg
d) 16 per kg

✔Answer

✔Solution

Correct Answer Is : 20 per kg

Solution Is : Let cost of 5 kg tea be = x cost of 8 kg sugar = ( 172 - x) Given, x * 120/100 + (172 - x) 110/100 = 199.20 x = 100 cost of 5 kg tea = 100 cost of tea per kg = 100/5 = 20

A sum of 6100₹ was divided among 8 men, 10 women and 12 children in such a way that each man received 25% more than a woman and each women received 25% more than a child. How much did each woman receive ?

a) 203.68
b) 206.08
c) 206.68
d) 201.68

✔Answer

✔Solution

Correct Answer Is : 206.08

Solution Is : Let woman received be x Man received = 125/100 x = 5/4 x and child received = 80/100 x = 4/5 x then 8 x (5/4 x) + 10 * x + 12 * ( 4/5 x) = 6100 148/5 x = 6100 x = 6100 * 5/148 = 206.08.

A shopkeeper sells his goods at 10% discount on the marked price. What price should he mark on an article that costs him 900 to gain 10% ?

a) 1050
b) 1100
c) 1150
d) 1000

✔Answer

✔Solution

Correct Answer Is : 1100

Solution Is : Let marked price be x SP = x * 90/100 = 9/10 x Again, SP = 900 * 110/100 = 990 9/10 x = 990 ⇒ x = 990 * 10/9 = 1100

In a survey of a town, it was found that 65% of the people surveyed watch the news on TV, 40% read a newspaper and 25% read a newspaper and watch the news on TV. What per cent of the people surveyed neither watch the news on TV nor read newspaper ?

a) 5%
b) 10%
c) 20%
d) 15%

✔Answer

✔Solution

Correct Answer Is : 20%

Solution Is :

The weight of the container alone is 25% of the container filled with a certain fluid. When some fluid is removed, then the weight of the container and the remaining liquid is 50% original total weight. What fractional part of the liquid has been removed?

a) 1/3
b) 2/3
c) 1/2
d) 3/4

✔Answer

✔Solution

Correct Answer Is : 1/3

Solution Is : (A) Suppose, weight of the container + fluid =100 kg Therefore, Weight of the container = 25 kg Weight of the fluid in the container = 75 kg

A machinist, by increasing his normal rate of work by 12 1/2% could produce 15 items more in a given period of time. How many times can he produce if he works at 80% of his normal rate?

a) 100
b) 90
c) 80
d) 96

✔Answer

✔Solution

Correct Answer Is : 96

Solution Is : ( D ) Suppose the normal rate of work = 100, in which the machinist can produce x items. Therefore, If the normal rate of work is increased to 112 1/2, then the machinist can produce (x+15) items. Therefore, ((x+15) / (112 1/2)) = (x/100) => x = 96

Which single discount will be equal to two successive discounts of 12% and 5%?

a) 15%
b) 7.50%
c) 16.40%
d) 12.20%

✔Answer

✔Solution

Correct Answer Is : 16.40%

Solution Is : Let initial amount be s100 on 12 % discount , Value = 100 x 88 /100 = Rs 88 On 5 % discount , Value = 88 x 95 / 100 = Rs , 83.6 Equal discount = 100 - 83.6/100 x 100 = 16.40 %

A book seller gives 12% discount on the printed price. What does a customer pay for a book with a printed price of ? 75?

a) ? 66
b) ? 64
c) ? 70
d) ? 63

✔Answer

✔Solution

Correct Answer Is : ? 66

Solution Is : Required price =88% of 75 =(75*88/100)(Here , 88 =100-discount) =?66

If marked price is ? 180 and price after discount is ?153, then the rate of discount is

a) 21%
b) 19%
c) 17%
d) 15%

✔Answer

✔Solution

Correct Answer Is : 15%

Solution Is : Discount =(180-153)=?27 so, per cent discount =(27*100/180)%=15%

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CDS Exam ELEMENTARY MATHEMATICS Study Material

Percentage Discount

If Ram got 30% marks and failed by 15 marks and Mohan got 40% and scored 35 more than pass marks. What is percentage necessary for passing ?

Correct Answer Is : 33%

Solution Is : Let maximum marks be x, then Given, Ram got pass marks = 30% of x + 15 = x * 30/100 + 15 Mohan got pass marks =x * 40/100 - 35 According to question, 3x + 150 = 4x - 350 x = 150 + 350 = 500 pass marks = 500 * 3/10 + 15 = 165 Necessary percentage for passing = 165/500 * 100 = 33%.

5 kg of tea and 8 kg of sugar together cost 172 ₹. The price of tea has risen by 20% and that of sugar by 10%. Hence the same quantities of tea and sugar now cost 199.20 ₹ . What is the original price of tea per kg ?

Correct Answer Is : 20 per kg

Solution Is : Let cost of 5 kg tea be = x cost of 8 kg sugar = ( 172 - x) Given, x * 120/100 + (172 - x) 110/100 = 199.20 x = 100 cost of 5 kg tea = 100 cost of tea per kg = 100/5 = 20

A sum of 6100₹ was divided among 8 men, 10 women and 12 children in such a way that each man received 25% more than a woman and each women received 25% more than a child. How much did each woman receive ?

Correct Answer Is : 206.08

Solution Is : Let woman received be x Man received = 125/100 x = 5/4 x and child received = 80/100 x = 4/5 x then 8 x (5/4 x) + 10 * x + 12 * ( 4/5 x) = 6100 148/5 x = 6100 x = 6100 * 5/148 = 206.08.

A shopkeeper sells his goods at 10% discount on the marked price. What price should he mark on an article that costs him 900 to gain 10% ?

Correct Answer Is : 1100

Solution Is : Let marked price be x SP = x * 90/100 = 9/10 x Again, SP = 900 * 110/100 = 990 9/10 x = 990 ⇒ x = 990 * 10/9 = 1100

In a survey of a town, it was found that 65% of the people surveyed watch the news on TV, 40% read a newspaper and 25% read a newspaper and watch the news on TV. What per cent of the people surveyed neither watch the news on TV nor read newspaper ?

Correct Answer Is : 20%

Solution Is :

The weight of the container alone is 25% of the container filled with a certain fluid. When some fluid is removed, then the weight of the container and the remaining liquid is 50% original total weight. What fractional part of the liquid has been removed?

Correct Answer Is : 1/3

Solution Is : (A) Suppose, weight of the container + fluid =100 kg Therefore, Weight of the container = 25 kg Weight of the fluid in the container = 75 kg

A machinist, by increasing his normal rate of work by 12 1/2% could produce 15 items more in a given period of time. How many times can he produce if he works at 80% of his normal rate?

Correct Answer Is : 96

Solution Is : ( D ) Suppose the normal rate of work = 100, in which the machinist can produce x items. Therefore, If the normal rate of work is increased to 112 1/2, then the machinist can produce (x+15) items. Therefore, ((x+15) / (112 1/2)) = (x/100) => x = 96

Which single discount will be equal to two successive discounts of 12% and 5%?

Correct Answer Is : 16.40%

Solution Is : Let initial amount be s100 on 12 % discount , Value = 100 x 88 /100 = Rs 88 On 5 % discount , Value = 88 x 95 / 100 = Rs , 83.6 Equal discount = 100 - 83.6/100 x 100 = 16.40 %

A book seller gives 12% discount on the printed price. What does a customer pay for a book with a printed price of ? 75?

Correct Answer Is : ? 66

Solution Is : Required price =88% of 75 =(75*88/100)(Here , 88 =100-discount) =?66

If marked price is ? 180 and price after discount is ?153, then the rate of discount is

Correct Answer Is : 15%

Solution Is : Discount =(180-153)=?27 so, per cent discount =(27*100/180)%=15%

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