Quantitative Aptitude PYQs

Given:

Woman takes 3 hours 20 minutes in two ways

Concept used:

Total time = T₁ + T₂

T₁ = Time taken by walking

T2 = Time taken by riding

Calculation:

According to the question,

She takes 2 hours less than actual if she rides both ways

Time for both ways = 3 hours 20 minutes – 2 hours

⇒ 1 hour 20 minutes

⇒ Time for one way = 40 minutes

Time for one way in walking =  3 hours 20 minutes – 40 minutes

⇒ 2 hours 40 minutes

∴ Half of the time she would take to walk both ways is 2 hours 40 minutes

Given:

A and B are paid Rs. 4400

A = 120% of B

Concept used:

Total = xA + yB

x and y are ratio

Calculation:

A = 120% of B

⇒ A = 6/5 of B

⇒ 5A = 6B

⇒ A/B = 6/5

⇒ A : B = 6 : 5

A + B = Rs. 4400

⇒ 11 units = 4400

⇒ 1 unit = 400

⇒ 5 units = 2000

⇒ B = Rs. 2000

∴ B paid Rs. 2000

Given:

Profit = 120% of the cost

Cost increases by 25%

Shortcut TrickLet's Assume the C.P be 100.

What % of the selling price is the profit,

⇒ (95/220) × 100 = 475/11 = 43.1 ≈ 43%

Alternate Method Concept used:

Profit = [(SP – CP)/CP] × 100

SP = selling price

CP = cost price

Calculation:

Let CP be Rs. 5x

Profit = 5x × 6/5

⇒ 6x

SP = 5x + 6x

⇒ 11x

New CP = 5x × 5/4

⇒ 25x/4

New profit = (11x – 25x/4)

⇒ 19x/4

Required % = (19x/4 ÷ 11x) × 100

⇒ 19/44 × 100

⇒ 43.18 ≈ 43%

∴ Required % is 43%

Given:

Interest increases = Rs. 3690

Interest rate increases 9% to \(13\frac{1}{2} %\)%

Shortcut Trick Difference of Interest rate = 13.5% - 9% = 4.5%

⇒ 4.5% = 3690

⇒ 1% = 820

⇒ 100% = 82,000

∴ The principal is Rs. 82000

Alternate Method

Formula used:

I = (P × t × r)/100

I = interest

P = principal

t = time period

r = rate of interest

Calculation:

Let P be Rs. x

[(x × 13.5 × 1)/100] – [(x × 9 × 1)/100] = 3690

⇒ [(13.5x – 9x)/100] = 3690

⇒ (4.5x)/100 = 3690

⇒ x = (3690 × 100)/4.5

⇒ x = 82000

⇒ P = Rs. 82000

∴ The principal is Rs. 82000

Given:

(x + y – z) : (y – z + 2w) : (2x + z – w) = 2 : 3 : 1

Calculation:

(x + y – z) : (y – z + 2w) : (2x + z – w) = 2 : 3 : 1

Here, From given ratio add 2 and 1 which is equal to 3.

⇒ (x + y – z) + (2x + z – w) = (y – z + 2w)

⇒ 3x + y – w = y – z + 2w

⇒ – 3w = – 3x – z

Now,

(5w – 3x – z) : 3w

⇒ (5w – 3w) : 3w

⇒ 2w : 3w

⇒ 2 : 3

∴ Required ratio is 2 : 3

Given:

The product of two numbers is 9216

Concept used:

The larger number is divided by the smaller number, the quotient is 16 leaving no remainder.

Larger number is 16 times of the smaller number

Calculation:

Let the smaller number be x

And larger number be 16x

According to the question,

The product of two numbers = 9216

⇒ (x × 16x) = 9216

⇒ x² = 9216/16

⇒ x2 = 576

⇒ x2 = 24²

⇒ x = 24

Now, The smaller number = x = 24

Larger number = 16x = 16 × 24 = 384

Difference = 384 – 24 = 360

∴ The difference between the numbers are 360.

Shortcut TrickAny number is divisible by both 5 and 10 only when the unit digit of a number is '0'.

Here, only 1 possibility by adding 8 to the number.

⇒ 3432 + 8 = 3440 

∴ The required number is 8.

Alternate MethodConcept used:

Any number that can be divided by a, b, c, and d is always a multiply a multiple of LCM(a, b, c, and d)

Calculation:

L. C. M of 10, 5, 4 and 2 = 20

On dividing 3432 by 20, the remainder is 12

Number to be added = 20 – 12 = 8

∴ The required number is 8.

Given:

Selling price = Rs. 2,230.40

Successive discount = 15%, 20% and 18%

Calculation:

Let the marked price = Rs. x

According to the question:

Selling price = [x × (100 – 15)/100 × (100 – 20)/100 × (100 – 18)/100]

⇒ 2,230.40 = (x × 85/100 × 80/100 × 82/100)

⇒ 2,230.40 = (1394x/2500)

⇒ x = (223040 × 2500)/(1394 × 100) = 4000

∴ The marked price (in Rs) of the article is Rs. 4000.

Given:

Number = 0.529, 2.01

Calculation:

The product of two number = 0.529 × 2.01 = 1.06329

According to the question:

Required difference = 1.06329 – 1 = 0.06329

∴ The required answer is 0.06329.

Given:

Dimensions of cuboid = 24.5 cm × 16.5 cm × 12 cm

Formula used:

Volume of cuboid = lbh

Where, l = length, b = breadth, h = height

Volume of sphere = (4/3)πr³

Concept used:

The solid sphere is formed by melting the Cuboid, their volumes will be equal

Calculation:

According to question:

Volume of cuboid = Volume of sphere

⇒ lbh = (4/3)πr3

⇒ 24.5 × 16.5 × 12 = (4/3) × (22/7) × r³

⇒ r3 = (245 × 165 × 12 × 3 × 7)/(4 × 22 × 100)

⇒ r3 = (49 × 3 × 3 × 7)/(4 × 2)

⇒ r3 = (7³ × 3³ × 2³)/(2³ × 2³)  

⇒ r = (7 × 3)/2 = 10.5

∴ The radius is 10.5 cm.

Given:

The sum of the squares of two positive numbers = 2426

The square root of one number = 7

Calculation:

Let numbers be x and y

⇒ √x = 7

⇒ x = 49

According to the question

⇒ x² + y² = 2426

⇒ (49)² + y2 = 2426

⇒ y2 = 2426 - 2401

⇒ y2 = 25

∴ The other number is 5.

Given:

The sum invested at 8% p.a. amounts to Rs. 20,280 at the end of one year, when the interest is compounded half-yearly.

Formula Used:

A = P(1 + R/100)^nT

A = Amount, P = Principal, R = Rate, T = Time

n = number of times interest compounded per year

Calculation:

Let Principal be Rs P

Interest is compounded half-yearly

⇒ Rate = 8/2 = 4%

According to the question

⇒ P(1 + \(\frac{4}{100}\) )² = 20280

⇒ P(104/100)² = 20280

⇒ P(26/25)² = 20280

⇒ P = \(\frac{20280 × 25 × 25}{26 × 26}\) = 18750 Rs

Again, according to the question

⇒ Amount = 18750(1 + \(\frac{8}{100}\))²

⇒ Amount = \(\frac{18750 × 27 × 27}{25 × 25}\) = 21870 Rs

⇒ CI = 21870 - 18750 = 3120

∴ Compound interest for 2 years at the same rate is 3120 Rs.

Given:

A shopkeeper marks his goods at 20% above the CP.

He sells three-fourth of the goods at the MP and the remaining at 30% discount on the MP.

Formula Used:

SP = MP × \(\frac{100-D}{100}\)

MP = Marked Price, SP = Selling Price, D = Discount

Calculation:

Let CP be Rs Y

⇒ MP = Y × \(\frac{120}{100}\)

SP of 3/4 goods = \(\frac{3}{4}\) × \(\frac{120}{100}\)Y = \(\frac{90}{100}\)Y

SP of remaining 1/4 goods = \(\frac{1}{4}\) × \(\frac{120}{100}\)Y × \(\frac{70}{100}\) = \(\frac{21}{100}\)Y

Total SP = \(\frac{90}{100}\)Y + \(\frac{21}{100}\)Y = \(\frac{111}{100}\)Y

Gain = \(\frac{111}{100}\)Y - Y = \(\frac{11}{100}\)Y

⇒ % Gain = \(\frac{(11/100)Y}{Y}\) × 100 = 11%

∴ % Gain is 11%.

Shortcut Trick 

Let,

Let, Total goods = 4 and Goods sold at MP = 3

So, Goods sold at DP = (4 - 3) = 1 

Now, Total CP = 4 × 100 = 400 units

Total SP = (3 × 120) + (1 × 84) = 360 + 84 = 444 units

So, Gain = (444 - 400)/400 × 100 = 44/4 = 11%

∴ His gain percentage is 11%.

Shortcut TrickWe can answer this question in a quick way by looking at the options.

Divisible by 12, 21, 35 means divisible by 3, 4, 5 and 7

Option 01: 212 - 2 = 210, not divisible by 4

Option 02: 844 - 2 = 842, not divisible by 5

Option 03: 632 - 2 = 630, not divisible by 4

Option 04: 422 - 2 = 420, divisible by 3, 4, 5, and 7, thus correct option.

Alternate Method

Given:

Numbers = 12, 21 and 35 

Remainder = 2

Concept Used:

We will find the LCM to get a number that is divisible by these numbers and then add the remainder to the LCM.

Calculation:

LCM of numbers 12, 21, and 35 = 420

⇒ Remainder = 2

Number = 420 + 2 = 422

∴ The least number which when divided by 12, 21, and 35 leaves the same remainder 2 is 422.

Given:

A borrows a sum of Rs.9,000 for 3 years at 5% simple interest

He lends it at simple interest to B at 7% for 3 years

Formula Used:

SI = (P × R × T)/100

SI = Simple Interest, P = Principal, R = Rate, T = Time

Calculation:

According to the question

SI = (9000 × 3 × 5)/100 = 1350 Rs

A lends to B at 7% for 3 years

SI = (9000 × 7 × 3)/100 = 1890 Rs

Profit = 1890 - 1350 = 540 Rs

∴ His gain is 540 Rs.

Given:

The side of rhombus is 10 cm and its diagonal is 12 cm.

Formula Used:

1. Area of triangle = \(\sqrt {s(s-a)(s-b)(s-c)} \) 

Where s = semi perimeter & a, b, and c are sides of the triangle

2. Area of rhombus (ABCD) = 2 × Area of Triangle 

Calculation:

Area of Δ ABC = \(\sqrt {s(s-a)(s-b)(s-c)} \)

Semi perimeter of Δ ABC (s) = (10 + 10 + 12) ÷ 2

Semi perimeter of Δ ABC (s) = 16

Area of Δ ABC = \(\sqrt {16(16-10)(16-10)(16-12)}\)

Area of Δ ABC = \(\sqrt {16 × 6 × 6 × 4} \) = 48 cm²

Area of rhombus (ABCD) = 2 × Area of Triangle = 96 cm²

∴ The area of rhombus is 96 cm².

Shortcut Trick 

We can answer this question by looking at the options

Option 4: Initial Speed = 40 km/hr, Increased Speed = 50 km/hrInitial Time = 400/40 = 10 hrs, New Time = 400/50 = 8 hrs

The given condition is satisfied

∴ The speed of the train is 40 km/hr.

Alternate Method

Given:

Distance = 400 km

Formula Used:

Distance = Speed × Time

Calculation:

Let speed be x km/hr

According to the question

\(\frac{400}{x}\) - \(\frac{400}{x+10}\) = 2 hours

⇒ 400 (\(\frac{1}{x}\) - \(\frac{1}{x+10}\)) = 2 

⇒ \(\frac{1}{x}\) - \(\frac{1}{x+10}\) = \(\frac{2}{400}\)

⇒ \(\frac{{10}}{{{x^{2;}} + 10x}}\)= \(\frac{1}{200}\)

⇒ \({x^2}\) + 10x - 2000 = 0

⇒ \({x^2}\) + 50x - 40x - 2000 = 0

⇒ x(x + 50) - 40(x + 50) = 0

⇒ (x + 50) (x - 40) = 0

⇒ x = 40 or -50

But speed can not be negative

∴ The speed of the train is 40 km/hr.

Given:

A is 5 times as good a workman as B

A  complete a job in 52 days less than B

Formula Used:

Total work = Total efficiency × Total days

Calculation:

 The ratio of efficiency of A & B is 5 : 1

Thus, the ratio of time of A & B is 1 : 5

Let time taken by A and B be T and 5T respectively

According to the question

⇒ 5T - T = 52 days

⇒ 4T = 52 days

⇒ T = 13 days

Total work = 13 × 5 = 65 units

A and B complete the work in 65/6 days

 ∴ While working together A & B will complete the work in \(10\frac{5}{6}\) days.

Concept:

Calculation:

⇒ \(\frac{{5.75 + \frac{5}{7};of;28 - 4.5}}{{\frac{3}{4};of;\left( {15.8 - 3.4} \right) + 5 \times 2.39}}\)

⇒ \(\frac{{5.75 + 20 - 4.5}}{{\frac{3}{4};of;\left( {12.4} \right) + 5 \times 2.39}}\)

⇒ \(\frac{5.75 + 20 - 4.5}{9.3 + 5 \times 2.39}\)

⇒ \(\frac{25.75 - 4.5}{9.3 + 11.95}\)

⇒ \(\frac{21.25}{21.25}\) = 1

∴ Answer is 1.

Shortcut Trick

Average of 75% number increases by 5

Average of 25% numbers decreases by 8

By mixture and Allegation method

Thus, the overall average increases by 1.75

⇒ New average = 36 + 1.75 = 37.5

∴ The new average of the total numbers is 37.75.

Alternate Method

Given:

The average of n number is 36

Formula Used:

Average = Sum of total observations ÷ Number of observations

Calculation:

Let n be 100

According to the question

Each of 75% of the numbers is increased by 5

New average of 75% of the numbers = 36 + 5 = 41

Sum of 75% of the numbers = 75 × 41 = 3075

Again, according to the question

Remaining numbers = 100 - 75 = 25

Average of remaining numbers decrease by 8

New average = (36 - 8) = 28

Sum of remaining numbers = 25 × 28 = 700

New average of all numbers = (3075 + 700) ÷ 100

⇒ (3075 + 700) ÷ 100 = 37.75

∴ The new average of the total numbers is 37.75.