Search Previous Year Questions

Given

In a low scoring T20 match the chasing team won by 10 wickets. the opener's age was 31 years and the first down was 11 years younger to him. The average of players who did not get their turn to bat is one year more than the overall average of the team. 

Concept used

Average

Calculation

T20 match was won by 10 wickets means no wicket fall.

Only the opening and one down batsmen played throughout.

As per the question,

Let the average of whole team be x

⇒ \(\frac{{11x\ -\ \left( {31\ +\ 20} \right)}}{9} = x + 1\)

⇒ 11x - 51 = 9x + 9

⇒ 2x = 60

⇒ x = 60/2 = 30 years.

The average of whole team = 30 years.

Given

An important project was to be submitted to the Headquarters. Clerk Sunil could type 40 pages in 8 hours whereas Clerk Abhishek could type 36 pages in 6 hours. If they start typing together on two different computers at 8:00 in the morning.

Concept used

Time and work

Calculation

Total work = n × Time 

n_Sunil = 40/8 = 5

n_Abhishek = 36/6 = 6

⇒ 121 = (5 + 6) × t

⇒ t = 121/11

⇒ t = 11 hrs.

⇒ 8 : 00 am + 11 hrs = 7 : 00 p.m

Given

A television of 21 inches placed in the cook house was replaced by a new television of 42 inches. 

Concept used

Percentage increase

Area of Square = (Side)²

Calculation

Area of Television

⇒ 21 × 21 = 441

Area of newly replaced television

⇒ 42 × 42

⇒ 1764

Change in area = 1764 - 441 = 1323

% increase = \(\frac{{1323}}{{441}} × 100 = 300% \)

∴ The percentage increase is 300%.

Concept:

A = \(\rm p[1 + \frac{r}{100}]^t \)

A = total amount

P = principal amount

r = rate of interest

t = time 

For quarterly , we get

\(\rm A = p[1 + \frac{r}{400}]^{4t} - P\)

Concept:

Given: Total amount = 19301, Principal amount = 12000 and rate of interest = 8%

\(\rm A = p[1 + \frac{r}{400}]^{4t} \)

⇒ \(\rm 19301 =12000[1 \ +\ \frac {8}{400}]^{4t} \)

⇒ \(\rm \frac {19301}{12000} =[1 \ +\ \frac {1}{50}]^{4t}\)

⇒ \(\rm \frac {19301}{12000} =[\frac {51}{50}]^{4t}\)

We can take an approximation value of t 

⇒ 1.6084 = (1.02)^4t

For t = 6 year

Given

Roman notation for 510

Calculation

Here 500 is denoted by D

10 is denoted by X

510 = DX

Given

At an online shopping site, the discount on an item 40% by the manufacturer. Then on top of that site gave additional discount of 20%. While making the payment the Credit Card company gave further discount of 5% on the transaction. 

Concept used

Profit and loss

Calculation

Discount on the mark price of an article always gives us selling price.

First discount of 40% = 3/5

Second discount of 20% = 4/5

Third discount of 5% = 19/20

As per the question,

⇒ \(246.24 = MRP \times \frac{3}{5} \times \frac{4}{5} \times \frac{{19}}{{20}}\)

⇒ MRP = Rs.540

Given

A vendor bought toffees at 6 for a rupee.

Concept used

Profit and loss

Calculation

Cost price of 1 toffee = Rs.6

Selling price of 1 toffee = 120 % of Rs.1

SP = 6/5

Rs.6/5 toffees sold is six

For Rs.1 toffee sold = (6 × 5/6) = 5

Given

One bus takes 7.5 h to move from A to B and another bus takes 9 h to move from A to C. If A is 300 km from B and 450 km from C

Concept used

Time and distance

Calculation

Distance of A to B is 300 km.

Time taken by bus to move from A to B = 7.5 hours

Speed = 300/7.5

Speed = 40 km/hr

Distance of A to C is 450 km.

Time taken by bus to move from A to C = 9 hours

Speed = 450/9

Speed = 50 km/hr

Ratio of speed = 40 : 50

Ratio of speed = 4 : 5

Given

The difference between 78% of a number and 59% of the same number is 323.

Concept used

Percentage

Calculation

As the number is same,

⇒ 78% - 59% = 19%

⇒ Given that difference of 19% = 323

1% = 323/19

⇒ 100% = 1700

As per the question,

⇒ 62% of 1700 

⇒ 62 × 17 = 1054

Given

Two ratios 2 : 3 and 4 : 5

Concept used

Ratio and proportion

Calculation

⇒ 2 : 3 = 2/3 × 100 = 66.66

⇒ 4 : 5 = 4/5 × 100 = 80

Out of two 4 : 5 is greater ratio.