Here are some quantitative questions that not solely helps you harden CDS (Combined Defence Services) entrance examination but for any of the govt. job examination.

So, try to solve on your own and then check for the answer enclosed under:

### Questions

**1. What is the remainder obtained once 1421 x 1423 x 1425 is divided by 12?**

a) 1 b) 2

c) 3 d) 4

**2. What is the remainder when 4 ^{96} is divided by 6?**

a) 4 b) 3

c) 2 d) 1

**3. A man rows downstream 32 km and 14 km upstream and he takes 6 hours to cover each distance. What is the speed of the current?**

a) 0.5 km/h b) 1 km/h

c) 1.5 km/h d) 2 km/h

**4. A train running at the speed of 72 km/h goes past a pole in 15 sec. What is the length of the train?**

a) 150 m b) 200 m

c) 300 m d) 350 m

**5. 2 men and 1 woman can complete a bit of labor in 14 days, while 4 women and 2 men can do the similar labor in 8 days. If a man gets ₹ 90 per day, what ought to be the wages per day of a woman?**

a) ₹ 48 b) ₹ 60

c) ₹ 72 d) ₹ 135

**6. 18 men can earn ₹ 360 in 5 days. How much cash can 15 men earn in 9 days?**

a) ₹ 600 b) ₹ 540

c) ₹ 480 d) ₹ 360

**7. In what proportion time would the simple interest on a principal amount be 0.125 times the principal amount at 10% per annum?**

a) 5/4 yr b) 7/4 yr

c) 9/4 yr d) 11/4 yr

**8. There is 60% increase in an amount in 6 yr at simple interest. What will be the compound interest on ₹ 12000 after 3 yr at the same rate of interest?**

a) ₹ 2160 b) ₹ 3120

c) ₹ 3972 d) ₹ 6240

**9. When an article is sold at 20% discount, the selling price is ₹ 24. What will be the selling price when the discount is 30%.**

a) ₹ 25 b) ₹ 23

c) ₹ 21 d) ₹ 20

**10. 16 L of a mixture contains milk and water in the ratio 5 : 3. If 4 L of milk is added to this mixture, the ratio of milk to water in the new mixture would be,**

a) 2 : 1 b) 7 : 3

c) 4 : 3 d) 8 : 3

### Answers

**1. (c)**

Solution: Instead to check the divisibility by 12. We check the divisibility by 3 and 4.

Here, we see that 1425 is divisible by 3. So, whole term is divisible by 3.

Again, we see that same of the number are divisible by 4. So, we divide each number by 4, we get remainder 1, 3 and 1. Now, we have to divide 1 x 1 x 3 by 4, get a remainder 3.

**2. (d)**

Solution: As we knows, that (x^{m} – a^{n}) is divisible by (x + a), for even values of m.

4^{96} = (4/1)^{96} = 4^{96}/1^{96} = (4^{96} – 1^{96}) is divisible by (4 + 1).

=> (4^{96} – 1) is divisible by 5.

**3. (c)**

Solution: Let speed of a boat in still water be x km/h and speed of the stream be y km/h

Then, speed of the boat downstream = (x + y) km/h

and speed of the boat upstream = (x – y) km/h

32/(x+y) = 6 [Speed=Distance/Time]

14/(x-y) = 6

=> 6x + 6y = 32 and 6x – 6y = 14

On solving equations, we get

x = 23/6 and y = 9/6 i.e. 1.5 km/h

**4. (c)**

Solution: Speed of train = Length of train / Time taken to cross the stationary object

= 72 x 1000 x 15 / 3600 = 300 m

**5. (b)**

Solution: 14 days work of 2 men and 1 woman = 8 days work of 4 women and 2 men

=> 1 day work of 28 men and 14 women = 1 day work of 32 women and 16 men

=> 28 men + 14 women = 32 women + 16 men

=> 28 m – 16 m = 32 w – 14 w

=> m / w = 3 / 2. So, efficiency of 1 man and 1 woman is 3 : 2

So, their wages must be in the same ratio

90/x = 3/2 [where, x = wages per day of a woman]

x = 60

**6. (b)**

Solution: Here, M_{1} = 18, D_{1} = 5, W_{1} = 360

and M_{2} = 15, D_{2} = 9, W_{2} = x (let)

M_{1}D_{1}W_{2} = M_{2}D_{2}W_{1}

=> 18 * 5 * x = 15 * 9 * 360

x = 540

**7. (a)**

Solution: Let the principal be ₹ x and the time be t yr.

Rate = 10%

Simple Interest = (P x R x T) / 100

0.125 x Principal = Simple interest

0.125 P = (P x 10 x T) / 100

T = 125 / 100 = 5/4

**8. (c)**

Solution: Let the principal be ₹x.

Then, SI = ₹ 60x / 100

SI = (P * R * T) / 100

=> 60x / 100 = (x * R * 6) / 100

Rate = 10%

Again principal = ₹ 12000, time = 3 yr

Interest = Principal (1 + Rate/100)^{Time} = 12000 (1 + 16/100)^{3}

= 12000 (11/100)^{3} = ₹ 15972

CI = Amount – Principal

= 15972 – 12000 = ₹ 3972

**9. (c)**

Solution: Let the cost price of article be ₹x.

Discount = 20% and selling price = 24

x = 24 + 20% of x

=> x = 24 + 20x/100

=> x = 24 + x/5 => x – x/5 = 24 => 4x/5 = 24

x = 30. So, cost price of an article is ₹ 30.

Now, selling price after 30% discount = 30 – 30% of 30

= 30 – (30/100) * 30 = ₹ 21

**10. (b)**

Solution: Given, total quantity of mixture = 16 L and ratio of milk and water = 5 : 3

Quantity of milk = (5 * 16) / (5+3) = 10 L and

Quantity of water = (3 * 16) / (5+3) = 6 L

If 4 L of milk is added to this mixture, then Quantity of milk = 10 + 4 = 14 L

and quantity of water = 6 L

New ratio = 14 : 6 = 7 : 3

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