Given:

Average of 30 children playing on weekdays

Average of 60 children playing on weekends

Concept used:

Calculation of overall average.

Solution:

Total number of children playing on weekdays in June = 30 × 20 = 600 (as June has 20 weekdays)

Total number of children playing on weekends in June = 60 × 10 = 600 (as June has 10 weekends)

Total number of children playing in June = 600 + 600 = 1200

Average number of children playing per day = Total number of children / Total days = 1200 / 30 = 40

Therefore, the average number of children playing per day in the park for June is 40.

Mistake Points

This question is from the official paper of SSC.

In most of the world, the workdays are from Monday to Friday and the weekend is from Saturday to Sunday. 

​So we have to consider Saturday and Sunday as weekends.

In June beginning with a Saturday, 10 weekends and 20 weekdays present.

Given:

(a - b) : (a + b) = 6 : 14

Concept:

Use the concept of ratios and proportions.

Solution:

⇒ a/b = 10/4 = 5/2

⇒ For the ratio (4a + 3b) : (4a - 3b), substitute a/b = 5/2.

⇒ (4a + 3b) : (4a - 3b) = (20 + 6) : (20 - 6) = 13 : 7

Therefore, the ratio (4a + 3b) : (4a - 3b) is 13 : 7.

Given:

The radius of the base of a cone is 7 cm.

The height is 15 cm.

Formula Used:

Calculation:

The volume of the cone as per the formula:

⇒ (1/3) × (22/7) × 7² × 15

⇒ 22/3 × 7 × 15

⇒ 22 × 7 × 5

⇒ 770cm³

∴ The volume of the cone is 770 cm³.

Shortcut Trick

Given:

The sum of a number and its reciprocal is 4.

Concept Used:

If a + 1/a = k

a² + 1/a² = k² - 2

Calculation:

Let the nuumber be a.

Reciprocal = 1/a

According to question,

⇒ a + 1/a = 4

⇒ a² + 1/a² = 4² - 2

⇒ a² + 1/a² = 14

∴ Option 3 is the correct answer.

Given data:

Initial ratio of seats for Engineering, Management and Science: 7 : 8 : 9

Proposed increase in seats: 20%, 30%, 60% respectively

Concept: To find the new ratio, increase each term in the ratio by its respective percentage and simplify if possible.

Calculation:

⇒ New ratio = 7 × (1+20/100) : 8 × (1+30/100) : 9 × (1+60/100)

⇒ 8.4 : 10.4 : 14.4

⇒ 21 : 26 : 36

Therefore, the ratio of the increased seats is 21 : 26 : 36.

Given:

Numbers = 0.09 and 0.64

Concept:

Mean proportional = √(Product of the numbers)

Solution:

⇒ Mean proportional = √(0.09 × 0.64) = 0.24

Therefore, the mean proportional between 0.09 and 0.64 is 0.24.

Given:-

CI - SI = 160

Rate of interest(r) = 20%

Time(t) = 3 years

Formula used:-

Ci = P[(1 + r/100)^t - 1]

SI = ( P × r × t)/100

Calculation:-

CI - SI = P[{(1 + 20/100)³ - 1} - {20 × 3}/100]

⇒ 160 = P[(6/5 × 6/5 × 6/5) - 1 - 6/10]

⇒ 160 = P[(2160 - 750 - 1250)/1250]

⇒ P = (160 × 1250)/160

⇒ P = 1250

Shortcut Trick

Calculation:-

Difference between CI and SI for 3 years,

∴ 160 = P(20/100)².(20/100 + 3)

⇒ 160 = P(1/5 × 1/5)(16/5)

⇒ P = 160 × (125/16)

⇒ P = 1250.

Given:

Simple interest = 3/5 of the principal

Time = 5 years

Formula used:

S.I = PRT/100

Calculation:

Time = 5 years

Let principal = 5x

Simple interest = 3x

Rate = R%

⇒ 3x = 5x × 5 × R/100

R = 12%

Given:

Discounted price of dining set = Rs. 17,640

Discount = 2%

Concept:

Original price = Discounted price/(1 - Discount%)

Solution:

⇒ Original price = Rs. 17,640/(1 - 2/100)

⇒ Original price = Rs. 18,000

Therefore, the original price of the dining set is Rs. 18,000.