Search Previous Year Questions

Given :

In a business A invested  = 15,000 Rs 

B invested  = 25,000 Rs. 

The end of the first year they earned a profit = 13000 Rs.

A left the business with his money after 6 months 

Calculation : 

In a business A invested for 6 months = 15000 × 6 = 90000 

In a business B invested for 12 month = 25000 × 12 = 300000 

A's share : B's share =  90000 : 300000 =  3 : 10 

Lets A's share = 3x

B's share = 10x 

According to what is given ,

⇒ 3x + 10x = 13000

⇒ 13x = 13000 

⇒ x = 1000 

A's share = 3x = 3 × 1000 = Rs.3000

∴ A's share is Rs.3000

Given,

Average weight of 50 boys = 45 kg

Formula:

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

Calculation:

Average weight of 50 boys = 45 kg

Sum of weight of 50 boys = 45 × 50 = 2250 kg

If 1 boys left the class, then average of 49 boys = 44.9 kg

Sum of weight of 49 boys = 44.9 × 49 = 2200.1

∴ Weight of boy who left the class = 2250 - 2200.1 = 49.9 kg

Alternate Solution

New average = 45 - 0.1 = 44.9 kg

Weight of boy left = New average + Number of total boys × Average reduced

= 44.9 + 50 × 0.1

= 44.9 + 5

= 49.9 kg

Shortcut Trick

Total Simple Interest = (P₁ × effective rate 1) + (P₂ × effective rate 2)

Effective Rate = Rate × Time

Total Interest = (14000 × 15%) + (19000 × 18%)

Total Interest = 2100 + 3420 = 5520

∴ The correct answer is ₹5,520.

Alternate Method

Given:

Principal 1 (P₁) = ₹14,000, Rate 1 (R₁) = 5%, Time (T) = 3 years

Principal 2 (P₂) = ₹19,000, Rate 2 (R₂) = 6%, Time (T) = 3 years

Formula Used:

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

Calculations:

⇒ SI₁ = (14000 × 5 × 3) ÷ 100 = 140 × 15 = ₹2100

⇒ SI₂ = (19000 × 6 × 3) ÷ 100 = 190 × 18 = ₹3420

⇒ Total Interest = SI₁ + SI₂

⇒ Total Interest = 2100 + 3420 = ₹5520

∴ The correct answer is ₹5,520.

Additional Information

Total Amount Formula

The total amount (A) after T years is given by A = P + SI = P × [1 + (R × T) ÷ 100].

Simple vs Compound Interest

In Simple Interest, the interest is calculated only on the initial principal. In Compound Interest, interest is calculated on both principal and the accumulated interest of previous periods.

Effective Rate Method

For Simple Interest, the effective rate for T years is simply R × T%. Here, 5% for 3 years becomes a 15% flat interest rate on the principal.

Given:

20% of voters did not vote 

invalids votes = 2800

the winner gets 53% of the valid votes and wins by 1200 votes

Calculations:

Let the total voting list = x

(x × 80% – 2800) × 6% = 1200

(∵ if the winner gets 53% votes then the loser gets 47% votes, the Difference between winner and loser is 6%)

⇒ (x × 80% - 2800) = 20000

⇒ x × 80% = 22800

⇒ x × 4/5 = 22800

∴ x = 28500

Given :

The total length of the bridge = 121 m

Time taken by train to cross a bridge = 62 sec

Time taken by train to cross a man standing = 51 sec

Formula used :

Speed of train = Distance/time

Calculation :

Let the total length of the train = x

⇒ speed of train = \({x + 121}\over 62\) = \(x\over51\)

⇒ 51x + 121 × 51 = 62x

⇒ 11x = 6171

⇒ x = \(6171\over11\) = 561

∴ The answer is 561 m.

GIVEN:

The population of town 4 years ago = 62500

Percentage increase annually = 20%

Time = 4 years

CONCEPT:

The percentage increase will be a successive percentage increase.

CALCULATION:

Population of village after 4 years = P × (1 + r/100)ⁿ

⇒ Population of village after 4 years = 62500 × (1 + 20/100)⁴

⇒ 62500 × 1296/625

= 129600

The answer is 1,29,600

Given:

Ratio of father and son age = 8 : 3

Ratio after 4 years = 11 : 5

Calculations:

Let the age of Father and Son three years before "8a" and "3a"

Age of Father and Son after 4 years from 3 years past = (8a + 7) and (3a + 7)

According to the question-

⇒ \(8a+7\over 3a+7\) = \(11\over 5\)

⇒ 40a + 35 = 33a + 77 

⇒ 7a = 42

⇒ a = 6

∴ Present age of Father = (8a + 3) = 8 × 6 + 3 = 51 years

∴ the present age of Father is 51 years.

Shortcut TrickAge ratio three years ago = 8 : 3

Age ratio (4 + 3) i.e. 7 years after = 11 : 5

Let the common ratio be Q.

40Q - 33Q = 77 - 35

⇒ 7Q = 42

⇒ Q = 6

⇒ 8Q = 48

⇒ 8Q + 3 = 51

Now, the present age of father = 51 years

∴ The present age of the father is 51 years.

Calculation : 

Ratio of BSNL Sim - Cards = 10

Ratio of Airtel Sim - Cards = 20

Ratio = 10 : 20

∴ The correct answer is 1 : 2.

Calculation : 

We know ,

⇒ 100% = 360° 

⇒ 1% = 3.6° 

Minimum angle = 10 × 3.6° = 36° 

∴ The correct answer is 36°.

The pattern followed here is:

Similarly,

Hence, the correct answer is “NKWDIPKF”.