Search Previous Year Questions

Given:

Principal = Rs. 7200, and Time = 2 years

Difference between SI and CI = Rs. 162

Concept used:

Difference = P$(\dfrac{R}{100})^2$

Explanation:

⇒ 162 = 7200 × $(\dfrac{R}{100})^2$

⇒ 162 = 7200 × $\dfrac{ R^{2} }{100× 100}$

⇒ r2 = 225

⇒ r = 15

∴ The rate of interest is 15%.

Formula Used:

Profit = Revenue – Expenditure

Percentage Revenue = Profit/Revenue × 100

Calculations:

Profit of company in 2014 = Rs.(150 – 130) cr

⇒ Profit of company in 2014 = Rs. 20 cr

Percentage Revenue = Profit/Revenue × 100

Percentage Revenue of company in 2014 = 20/150 × 100 = 13.33%      ----(1)

Profit of company in 2015 = Rs.(210 – 150) cr

⇒ Profit of company in 2015 = Rs. 60 cr

Percentage Revenue of company in 2015 = 60/210 × 100 = 28.57%      ----(2)

Profit of company in 2016 = Rs.(200 – 175) cr

⇒ Profit of company in 2016 = Rs. 25 cr

Percentage Revenue of company in 2016 = 25/200 × 100 = 12.5%      ----(3)

Profit of company in 2017 = Rs.(240 – 200) cr

⇒ Profit of company in 2017 = Rs. 40 cr

Percentage Revenue of company in 2017 = 40/240 × 100 = 16.67%      ----(4)

Profit of company in 2018 = Rs.(220 – 165) cr

⇒ Profit of company in 2018 = Rs. 55 cr

Percentage Revenue of company in 2018 = 55/220 × 100 = 25%      ----(5)

Profit of company in 2019 = Rs.(255 – 170) cr

⇒ Profit of company in 2019 = Rs. 85 cr

Percentage Revenue of company in 2019 = 85/255 × 100 = 33.33%      ----(6)

We observe that only (2) and (6) have profit more than 25%

⇒ Number of years in which profit is more than 25% = 2

∴ The number of years in which profit is more than 25% is 2.

Given:

Total Distance = 270 km

In the first 4 hours, its speed is 50 km/h and it decreases to 35 km/h in the remaining journey.

Formula Used:

Average Speed = Total Distance/Total Time

Calculation:

Total Distance = 270 km

In the first 4 hours, its speed is 50 km/h

⇒ Disatnce covered = 50 × 4 = 200 km

Remaining diatance covered in 35 km/h

⇒ Time = (270 - 200)/35

⇒ 2 h

Total Time = 4 + 2 = 6 h

Average speed = 270/6

⇒ 45 km/h

∴ The average speed of the bike is 45 km/h.

Given:

An equilateral triangle sides are 16 cm each.

Concept used:

The area of an equilateral triangle is, √3 / 4 × a2 

Calculation:

The area of an equilateral triangle is

√3 / 4 × 16² = 64√3 cm2

∴ The correct option is 3

Given:

a + b + c = 6

a2 + b2 + c2 = 32

a3 + b3 + c3 = 189

Formula used:

x³ + y³ + z³ - 3xyz = (x + y + z) [x² + y² + z² - (xy + yz + zx)]

(x + y + z)² = x2 + y2 + z2 + 2 (xy + yz + zx)

Calculation:

(a + b + c)2 = a2 + b2 + c2 + 2 (ab + bc + ca)

⇒ 6² = 32 + 2 (ab + bc + ca)

⇒ 36 = 32 + 2 (ab + bc + ca)

⇒ 2 (ab + bc + ca) = 36 - 32 = 4

⇒ (ab + bc + ca) = 4/2 = 2

Also, a3 + b3 + c3 - 3abc = (a + b + c) [a2 + b2 + c2 - (ab + bc + ca)]

⇒ 189 - 3abc = 6 (32 - 2)

⇒ 189 - 3abc = 6 × 30

⇒ 3abc = 189 - 180 = 9

⇒ abc = 9/3 = 3

⇒ abc - 3 = 3 - 3 = 0

∴ The value of abc - 3 is 0

Shortcut Trick

Extra interest % = Rate increase × Time

Extra interest % = 5% × 4 = 20%

Given, 20% of Sum = ₹520

⇒ 100% of Sum = 520 × 5 = ₹2,600

∴ The correct answer is ₹2,600.

Alternate Method

Given:

Time (T) = 4 years

Increase in Rate (R_diff) = 5%

Increase in Interest (I_diff) = ₹520

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Calculations:

⇒ Let the Principal be P and original Rate be R.

⇒ New Interest − Old Interest = 520

⇒ [(P × (R + 5) × 4) ÷ 100] − [(P × R × 4) ÷ 100] = 520

⇒ (4P ÷ 100) × [R + 5 − R] = 520

⇒ (4P ÷ 100) × 5 = 520

⇒ 20P ÷ 100 = 520

⇒ P ÷ 5 = 520

⇒ P = 520 × 5

⇒ P = 2,600

∴ The correct answer is ₹2,600.

Additional Information

Simple Interest Property

Simple interest is calculated only on the Principal amount, making it constant for every year if the rate remains unchanged.

Rate-Time Relationship

The total change in interest is directly proportional to the product of the change in rate and total time.

Principal Formula

Principal (P) = (100 × SI) ÷ (R × T). This can be used to find the sum when interest, rate, and time are known.

Given:

A ∶ B ∶ C = 5 ∶ 7 ∶ 11

B gets Rs. 1500 more than A.

Concept:

Proportional distribution

Solution:

⇒ The ratio of B to A is 7 : 5.

⇒ The difference in shares is 2 parts.

⇒ So, 2 parts = Rs. 1500, then 1 part = Rs. 1500 / 2.

⇒ Hence, B's share = 7 parts × (Rs. 1500 / 2).

Therefore, B's share is Rs. 5250.

Given:

Edge = 30 cm

Concept used:

SA of sphere = 4πr²

Calculation:

Radius = 30/2 = 15 cm

Surface Area of sphere = 4 × 3.14 × 15 × 15 = 2826 cm²

∴ The surface area of the largest possible sphere that can be carved out is 2826 cm².

Given: Principal = Rs 15000 and Amount = Rs 18150

Let the rate be r%

⇒ A = P(1 + r/100n)^nt

⇒ 18150 = 15000(1 + r/100)²

⇒ 1.21 = (1 + r/100)²

Taking square root on both sides

⇒ 1.1 = 1 + r/100

 ⇒ 0.1 × 100 = r

∴ r = 10

Concept Used :

A number will be divided by three if sum of all the digits in a number is multiple of 3.

For eg : 234 = 2 + 3 + 4 = 9, and here 9 is the multiple of 3.

Calculation :

⇒ 34623 = 3 + 4 + 6 + 2 + 3 = 18 , Multiple of 3

⇒ 34716 = 3 + 4 + 7 + 1 + 6 = 21 , Multiple of 3

⇒ 34782 = 3 + 4 + 7 + 8 + 2 = 24, Multiple of 3

⇒ 34783 = 3 + 4 + 7 + 8 + 3 = 25 , Not a multiple of 3

∴ The correct answer is 34783.