OSSSC Math Test – 03

Given:

Number of terms = 49

First term = 51

Last term = 99

Formula used:

Average = (Sum of observations) / (Number of observations)

Sum of n terms in AP = (n/2)[a + l]

Where, AP = Arithmetic progression,

n = number of terms, a = first term

and l = last term

Calculation:

Total number b/w 50 & 100 = 49

Therefore,

a = 51, l = 99, n = 49

Sum = (49/2)[51 + 99]

⇒ Sum = (49/2) × 150

⇒ Sum = 3675

Average = Sum / Number of terms

⇒ Average = 3675 / 49

⇒ Average = 75

∴ The average of all natural numbers lying between 50 and 100 is 75.

Given:

Money distributed among A, B, C, D in the ratio 7 ∶ 5 ∶ 4 ∶ 2

And C gets Rs. 500 more than D

Calculation:

Let A, B, C, and D be 7x, 5x, 4x and 2x respectively.

According to the question,

C gets Rs. 500 more than D. So,

4x - 2x = 500

⇒ 2x = 500

⇒ x = 250

Now we calculate all values

A = 7x = 7× 250 = Rs. 1750

B = 5x = 5 × 250 = Rs. 1250

C = 4x = 4 × 250 = Rs. 1000

D = 2x = 2 × 250 = Rs. 500

∴ The share of B will be Rs. 1250

Calculation:

P : Q = 9 : 1,

Multiplied by 8 (to match with the 'Q : R' ratio)

⇒ P : Q = 72 : 8

⇒ Q : R = 1 : 8

Now, P : R = 72 : 64

R : S = 1 : 10,

Multiplied by 64 (to match with the 'P : R' ratio)

⇒ R : S = 64 : 640

⇒ P : R : S = 72 : 64 : 640

∴ The required ratio P: R : S  is 9 : 8 : 80.

Given:

A person travels three equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr.

Total time = 47 minutes.

Formula used:

Distance = Speed × Time.

Average speed = Total distance/Time.

Calculation:

Let the total distance traveled be 3X .

Then every distance of X will be simultaneously cover with 3 km/hr, 4 km/hr and 5 km/hr.

Total time = 47 minutes, = 47/60 hrs.

Total time required for traveling 3X km = X/3 + X/4 + X/5.

⇒ X/3 + X/4 + X/5 = 47/60

⇒ 47X/60 = 47/60

⇒ X = 1

Total distance = 3X = 3 × 1 = 3

∴ The total distance is 3 km.

The least number divisible by 40, 45, 50 and 60 is the L.C.M of the numbers

L.C.M of (40, 45, 50, 60) = 1800

Now, let the required number be N

According to the question,

N² × 50 = 1800

⇒ N² = 36

∴ N = 6

Given:

Ram spends 20%, 15%, 25% and 20% of his salary on rent, education, food and medicine & entertainment respectively.

His monthly saving is Rs. 5000

Calculation:

Let the total salary be x

Total percent of salary spent on rent, education, food and medicine & entertainment = (20 + 15 + 25 + 20)%

⇒ 80%

Remaining salary = (100 - 80)%

⇒ 20%

According to the question, we have

20% of x = Rs. 5000

⇒ (20/100) × x = Rs. 5000

⇒ x = Rs. (5000 × 5)

⇒ x = Rs. 25000

So, money spent on education = 15% of Rs. 25000

⇒ (15/100) × Rs. 25000

⇒ Rs. 3750

∴ Ram spends Rs. 3750 on education.

Given:

Time period = 10 years

Formula used:

SI = (P × R × T)/100

A = P + SI

Where, P = principal, R = rate, T = time, SI = simple interest

Calculations:

The sum of money is 2P

SI = 2P - P

⇒ P = (P × R × 10)/100

⇒ 1 = R/10

⇒ R = 10%

∴ The rate of interest is 10%.

Given

Average marks of 210 students = 45

Average marks of failed students = 27

Average marks of passed students = 54

Formula:

Average = Sum of all observations/total number of all observations

Calculation:

Let number of failed students be x, then

Number of passed students = 210 – x

According to the question

x × 27 + (210 – x) × 54 = 210 × 45

⇒ 27x + 11340 – 54x = 9450

⇒ 54x – 27x = 11340 – 9450

⇒ 27x = 1890

⇒ x = 1890/27

⇒ x = 70

Number of passed students = 210 - 70 = 140

∴ The number of passed students is 140.

Given: 

The compound interest for one year = Rs. 200

The compound interest for 2^nd year = Rs. 240

Concept Used:

In the case of compound interest, the extra interest of the second year is the interest on the interest in the first year.

Calculation:

Let the rate of interest be R%

According to the question, we have

The difference between the interest of 2nd and 1st year = 240 - 200

⇒ Rs. 40

Now, The principal of the extra interest of 2nd year is the interest on the first year

⇒ The interest on Rs. 200 for 1 year is Rs. 40

According to the question,

(200 × R × 1)/100 = 40   [∵ For 1 year simple interest and compound interest are same]

⇒ 200 × R = 40 × 100

⇒ R = 20%

∴ The rate of interest is 20%

Given:

The cost price of the T.V = Rs. 17,000

Profit = 8%

Formula Used:

Selling price = [(100 + Profit)/100] × Cost price

Calculation:

According to the given question,

Selling price = [(100 + 8)/100] × 17,000

⇒ (108/100) × 17,000

⇒ Rs. 18,360

∴ The selling price of the T.V is Rs. 18,360.

Given:

P and Q can complete a work in 16 days

Q and R can complete a work in 24 days

R and P can complete work in 10 days

Concept used:

P can complete a work in n days so, 1 days work will be 1/n

Calculation:

According to question,

2(P + Q + R) → 1 days work

⇒ 1/16 + 1/24 + 1/10

⇒ (15 + 10 + 24)/240

⇒ 49/240 part

P + Q + R →  one day work = 49/(240 × 2)

⇒ 49/480 part

Number of days required to complete work = 480/49

∴ The work will be finished in 480/49 days

Given:

The ratio of two numbers = 5 : 4

First number × 40% = 120

Calculation:

Let common factor of the numbers be x then numbers be 5x and 4x

According to question,

5x × 40% = 120

⇒ 5x × 40/100 = 120

⇒ x = 60

First number 5x = 5 × 60 = 300

Second number = 4x = 4 × 60 = 240

60% of second number = 240 × 60/100

⇒ 60% of second number = 144

∴ 60% of second number is 144.

Given:

Product of digits of a two-digit number is 8

Adding 18 reverse the number

Calculation:

Let digit on number be a and b

So, the number is a × 10 + b

According to question

⇒ a × 10 + b + 18 = b × 10 + a

⇒ 10a – a + b – 10b = 18

⇒ 9a – 9b =18

⇒ a – b = 2

Now we look at the factors of 8 with a difference of 2

⇒ 4 × 2 = 8

So, a = 2 and b =

number will be 2 × 10 + 4 = 24

∴ The number is 24

Given:

Discounts are 8%, 10%, and 12%

Concept used:

Discount is given on marked price

Formula used:

Equivalent discount = (-D₁ + (-D₂) + (D₁D₂)/100)

Calculation:

Taking D₁ = 8% and D₂ = 10% and D₃ = 12%

Equivalent discount of 8% and 10% = -8 + (-10) + (8 × 10)/100

⇒ -18 + 0.8 = -17.2%

Equivalent discount of 17.2% and 12% = -17.2 + (-12) + (17.2 × 12)/100 = 27.136

∴ The equivalent discount is 27.136%