# Quantitative Reasoning Questions for MAH-CET PDF

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**Question 1:Â **The rate of onion increased from â‚¹ 70 per kilogram to â‚¹ 120 per kilogram within a month. By what percentage (approximate) did the rate of onion increase?

a)Â 75.2%

b)Â 65%

c)Â 80%

d)Â 71.5%

**1)Â AnswerÂ (D)**

**Solution:**

Percentage increase in the rate of onion =Â $\frac{120-70}{70}\times100$

=Â $\frac{50}{70}\times100$

=Â $\frac{500}{7}$

= 71.43%

= 71.5% (approximately)

Hence, the correct answer is Option D

**Question 2:Â **Which two signs and two numbers should be interchanged to make the given equation correct?

$16 + 8 \times 25 – 15 \div 5 = 138$

a)Â $\times$ and $+$; 15 and 25

b)Â $\div$ and $-$; 15 and 5

c)Â $\times$ and $-$; 8 and 25

d)Â $\times$ and $+$; 8 and 25

**2)Â AnswerÂ (A)**

**Solution:**

By Trial and Error method,

__Option A__

$16\times8+15-25\div5=138$

$16\times8+15-5=138$

$128+15-5=138$

$138=138$

Hence, the correct answer is Option A

**Question 3:Â **Select the correct equation when the signs â€˜+â€™ and $â€˜\timesâ€™$ and the numbers â€˜4â€™ and â€˜8â€™ are interchanged.

a)Â $12 \times 4 + 8 = 34$

b)Â $6 + 8 \times 4 = 38$

c)Â $2 \times 4 + 8 = 34$

d)Â $4 + 8 \times 2 = 32$

**3)Â AnswerÂ (C)**

**Solution:**

By Trial and Error method,

__Option A__

$12+8\times4=34$

$12+32=34$

$44=34$

Hence Option A is incorrect

__Option B__

$6\times4+8=38$

$24+8=38$

$32=38$

Hence Option B is incorrect

__Option C__

$2+8\times4=34$

$2+32=34$

$34=34$

Hence, the correct answer is Option C

**Question 4:Â **Train â€˜Aâ€™ runs at a speed of 80 kmph and leaves station â€˜Xâ€™ at 11.00 a.m. Train â€˜Bâ€™ leaves station â€˜Xâ€™ at 11.15 a.m.in the same direction, on the same day . At what speed train â€˜Bâ€™ should run in order to catch train â€˜Aâ€™ at station â€˜Yâ€™ located at a distance of 60 km?

a)Â 120 km/h

b)Â 125 km/h

c)Â 115 km/h

d)Â 110 km/h

**4)Â AnswerÂ (A)**

**Solution:**

Speed of train A = 80 km/h

Distance between station X and station Y = 60 km

Time taken by train A to reach station Y = $\frac{60}{80}$ hours = $\frac{3}{4}$ hoursÂ $\frac{3}{4}\times$60 minutes = 45 minutes

Since train B starts 15 min late, it should reach station Y in 30 minutes to catch train A at station Y.

Time taken by train B to reach station Y = 30 minutes =Â $\frac{1}{2}$ hour

$\therefore\ $Speed of train B =Â $\frac{\text{Distance from station X to station Y}}{\text{Time}}$ = $\frac{60}{\frac{1}{2}}$ =Â 120 km/h

Hence, the correct answer is Option A

**Question 5:Â **Which two numbers should be interchanged in the following equation to make it correct?

$36 \div 6 – 15 \times 2 + 48 = 14$

a)Â 36 and 48

b)Â 6 and 14

c)Â 48 and 15

d)Â 2 and 6

**5)Â AnswerÂ (A)**

**Solution:**

By Trial and Error method,

__Option A__

$48\div6-15\times2+36=14$

$8-15\times2+36=14$

$8-30+36=14$

$14=14$

Hence, the correct answer is Option A

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**Question 6:Â **In a class, every student participated in one of the three activities i.e. folk song, kathak and quiz. 22% of the total students participated in folk song. 25% of the remaining students participated in kathak. The remaining students participated in quiz. What percentage of students participated in quiz?

a)Â 53%

b)Â 30.6%

c)Â 41.5%

d)Â 58.5%

**6)Â AnswerÂ (D)**

**Solution:**

Let the total number of students = T

22% of the total students participated in folk song

Number of students participated in folk song =Â $\frac{22}{100}$T

Remaining students = T –Â $\frac{22}{100}$T =Â $\frac{78}{100}$T

25% of the remaining students participated in kathak

Number of students participated in kathak = $\frac{25}{100}\times\frac{78}{100}$T =Â $\frac{39}{200}$T

Remaining students participated in quiz.

Number of students participated in quiz = T – $\frac{22}{100}$T – $\frac{39}{200}$T = $\frac{117}{200}$T

Percentage of students participated in quiz = $\frac{\frac{117}{200}T}{T}\times100$ = 58.5%

Hence, the correct answer is Option D

**Question 7:Â **A person is employed to a company on salary of â‚¹ 6,000 per month. Through out the year, he remained absent from work for 15 days. If â‚¹ 200 gets deducted for every single holiday, then how much money will he earn at the end of the year ?

a)Â â‚¹ 72,000

b)Â â‚¹ 70,000

c)Â â‚¹ 69,000

d)Â â‚¹ 75,000

**7)Â AnswerÂ (C)**

**Solution:**

Salary of the person per month =Â â‚¹ 6,000

Salary of the person per year =Â $6000\times12$ =Â â‚¹ 72,000

Deduction for 1 holiday =Â â‚¹ 200

Deduction for 15 holidays = $15\times200$ = â‚¹ 3,000

$\therefore\ $Money earned by the person at the end of the year = 72000 – 3000 = â‚¹ 69,000

Hence, the correct answer is Option C

**Question 8:Â **What will be the value of â€˜a + bâ€™ in the following equation?

$\left[4 \left(3 + \left\{9 \times 6 \div 3 + \left\{12 \div \left(1 \div 1 \times 3\right)\right\}\right\}\right)\right] = 5^a \times 2^b$

a)Â 5

b)Â 6

c)Â 7

d)Â 4

**8)Â AnswerÂ (D)**

**Solution:**

$\left[4\left(3+\left\{9\times6\div3+\left\{12\div\left(1\div1\times3\right)\right\}\right\}\right)\right]=5^a\times2^b$

$\Rightarrow$ Â $\left[4\left(3+\left\{9\times6\div3+\left\{12\div\left(1\times3\right)\right\}\right\}\right)\right]=5^a\times2^b$

$\Rightarrow$ Â $\left[4\left(3+\left\{9\times6\div3+\left\{12\div3\right\}\right\}\right)\right]=5^a\times2^b$

$\Rightarrow$ Â $\left[4\left(3+\left\{9\times6\div3+4\right\}\right)\right]=5^a\times2^b$

$\Rightarrow$ Â $\left[4\left(3+\left\{9\times2+4\right\}\right)\right]=5^a\times2^b$

$\Rightarrow$ Â $\left[4\left(3+\left\{18+4\right\}\right)\right]=5^a\times2^b$

$\Rightarrow$ Â $\left[4\left(3+22\right)\right]=5^a\times2^b$

$\Rightarrow$ Â $\left[4\left(25\right)\right]=5^a\times2^b$

$\Rightarrow$ Â $100=5^a\times2^b$

$\Rightarrow$ Â $25\times4=5^a\times2^b$

$\Rightarrow$ Â $5^2\times2^2=5^a\times2^b$

Comparing both sides,Â a = 2 and b = 2

$\therefore\ $a + b = 2 + 2 = 4

Hence, the correct answer is Option D

**Question 9:Â **One pound is approximately equal to 0.453 kg. Jennifer bought 4.409 pounds of custard apple. How many kilograms of custard apple did she buy (approximately)?

a)Â 2

b)Â 1

c)Â 1.5

d)Â 2.5

**9)Â AnswerÂ (A)**

**Solution:**

Given,Â One pound is approximately equal to 0.453 kg

Custard apple bought by Jennifer = 4.409 pounds = 4.409 x 0.453 kg = 1.997 kg = 2 kg (approximately)

Hence, the correct answer is Option A

**Question 10:Â **Select the correct combination of mathematical signs to replace ‘Yâ€™ sequentially and balance the following equation.

18 Y 2 Y 3 Y 3 Y 9

a)Â $\times, =, -, \div$

b)Â $\times, \div, +, =$

c)Â $\div, \times, =, -$

d)Â $\div, \times, =, \times$

**10)Â AnswerÂ (D)**

**Solution:**

By Trial and Error method,

__Option A__

$18\times2=3-3\div9$

$18\times2=3-\frac{1}{3}$

$36=3-\frac{1}{3}$

$36=\frac{8}{3}$

Hence Option A is incorrect

__Option B__

$18\times2\div3+3=9$

$18\times\frac{2}{3}+3=9$

$12+3=9$

$15=9$

Hence Option B is incorrect

__Option C__

$18\div2\times3=3-9$

$9\times3=3-9$

$27=-6$

Hence Option C is incorrect

__Option D__

$18\div2\times3=3\times9$

$9\times3=3\times9$

$27=27$

Hence, the correct answer is Option D

**Question 11:Â **Which two signs and numbers should be interchanged to make the following equation correct?

$16 \times 18 + 2 – 14 \div 3 = 38$

a)Â 14 and 18, + and –

b)Â 16 and 14, – and $\times$

c)Â 14 and 18, + and $\times$

d)Â 16 and 3, – and $\div$

**11)Â AnswerÂ (C)**

**Solution:**

By Trial and Error method,

__Option A__

$16\times14-2+18\div3=38$

$16\times14-2+6=38$

$224-2+6=38$

$228=38$

Hence Option A is incorrect

__Option B__

$14-18+2\times16\div3=38$

$14-18+2\times\frac{16}{3}=38$

After solving the value will be decimal which is not possible

__Option C__

$16+14\times2-18\div3=38$

$16+14\times2-6=38$

$16+28-6=38$

$38=38$

Hence, the correct answer is Option C

**Question 12:Â **Which two signs should be interchanged to make the following equation correct?

$4 \div 6 + 9 – 48 \times 8 = 27$

a)Â + and $\times$

b)Â + and –

c)Â $\div$ and +

d)Â $\div$ and $\times$

**12)Â AnswerÂ (D)**

**Solution:**

By Trial and Error method,

__Option A__

$4\div6\times9-48+8=27$

$\frac{2}{3}\times9-48+8=27$

$6-48+8=27$

$-34=27$

Hence Option A is incorrect

__Option B
__

$4\div6-9+48\times8=27$

$\frac{2}{3}-9+48\times8=27$

After solving the value will be decimal which is not possible

__Option C__

$4+6\div9-48\times8=27$

$4+\frac{2}{3}-48\times8=27$

After solving the value will be decimal which is not possible

__Option D__

$4\times6+9-48\div8=27$

$4\times6+9-6=27$

$24+9-6=27$

$27=27$

Hence, the correct answer is Option D

**Question 13:Â **A and B can do a piece of work in 30 days and 18 days respectively. A started the work alone and then after 6 days B joined him till the completion of the work. In how many days has the whole work completed?

a)Â 17

b)Â 15

c)Â 9

d)Â 12

**13)Â AnswerÂ (B)**

**Solution:**

Let the total work be W

Number of days required for A to complete the work = 30 days

$\Rightarrow$Â Work done by A in 1 day =Â $\frac{W}{30}$

Number of days required for B to complete the work = 18 days

$\Rightarrow$ Â Work done by B in 1 day = $\frac{W}{18}$

Work done by A and B together in 1 day =Â $\frac{W}{30}+\frac{W}{18}$ =Â $\frac{3W+5W}{90}$ =Â $\frac{4W}{45}$

Work done by A alone in 6 days =Â $\frac{W}{30}\times6$ =Â $\frac{W}{5}$

Remaining work =Â $W-\frac{W}{5}$ =Â $\frac{4W}{5}$

Number of days required for both A and B to complete remaining work =Â $\frac{\text{Remaining work}}{\text{Work in 1 day}}$ = $\frac{\frac{4W}{5}}{\frac{4W}{45}}$ = 9 days

$\therefore\ $Number of days required to complete the whole work = 6 + 9 = 15 days

Hence, the correct answer is Option B

**Question 14:Â **Which two signs should be interchanged to make the given equation correct?

$(72 \div 18) + 30 \times 8 – 4 = 20$

a)Â + and –

b)Â + and $\times$

c)Â $\times$ and $\div$

d)Â + and $\div$

**14)Â AnswerÂ (D)**

**Solution:**

By Trial and Error method,

__Option A__

$(72\div18)-30\times8+4=20$

$4-30\times8+4=20$

$4-240+4=20$

$-232=20$

Hence Option A is incorrect

__Option B__

$(72\div18)\times30+8-4=20$

$4\times30+8-4=20$

$120+8-4=20$

$124=20$

Hence Option B is incorrect

__Option C
__

$(72\times18)+30\div8-4=20$

$1296+30\div8-4=20$

$1296+3.75-4=20$

After solving theÂ value will be decimal which is not possible

__Option D__

__$(72+18)\div30\times8-4=20$__

$90\div30\times8-4=20$

$3\times8-4=20$

$24-4=20$

$20=20$

Hence, the correct answer is Option D

**Question 15:Â **Which two signs or numbers need to be interchanged to make the following equation correct?

$(18 \div 9) + 9 \times 8 = 24$

a)Â $+, \times$

b)Â $+, \div$

c)Â $\times, \div$

d)Â $18, 8$

**15)Â AnswerÂ (B)**

**Solution:**

By Trial and Error method,

__Option A__

$(18\div9)\times9+8=24$

$2\times9+8=24$

$18+8=24$

$26=24$

Hence Option A is incorrect

__Option B__

$(18+9)\div9\times8=24$

$27\div9\times8=24$

$3\times8=24$

$24=24$

Hence, the correct answer is Option B

**Question 16:Â **If â€˜#â€™ means â€˜â€”â€™, â€˜&â€™ means â€˜$\div$â€™, â€˜@â€™ means â€˜$\times$â€™ and â€˜$\div$â€™ means â€˜+â€™, then 15 @ 2 $\div$ 900 & 30 # 10 = ?

a)Â 21

b)Â 310

c)Â 50

d)Â 600

**16)Â AnswerÂ (C)**

**Solution:**

By applying the given conditions,

$15$ @ $2$ $\div$ $900$ & $30$ # $10$ $=15\times2\ +900 \div 30 -10$

$=15\times2\ +30\ -10$

$=30+30\ -10$

$=50$

Hence, the correct answer is Option C

**Question 17:Â **Which two numbers should be interchanged in the following equation to make it correct?

$6 + 28 \div 4 – 2 \times 17 = 12$

a)Â 17 and 4

b)Â 28 and 2

c)Â 17 and 6

d)Â 6 and 4

**17)Â AnswerÂ (C)**

**Solution:**

By Trial and Error method,

__Option A__

$6+28\div17-2\times4=12$

$6+\frac{28}{17}-2\times4=12$

After solving the value will be decimal which is not possible. Hence Option A is incorrect.

__Option B__

$6+2\div4-28\times17=12$

$6+0.5-28\times17=12$

After solving the value will be decimal which is not possible. Hence Option B is incorrect.

__Option C__

$17+28\div4-2\times6=12$

$17+7-2\times6=12$

$17+7-12=12$

$12=12$

Hence, the correct answer is Option C

**Question 18:Â **Aman has an equal number of one, five, ten and twenty rupee bank notes, to make a total of â‚¹ 1,080. How many bank notes does Aman have in total?

a)Â 100

b)Â 90

c)Â 120

d)Â 105

**18)Â AnswerÂ (C)**

**Solution:**

Let the number of one rupee notes with the Aman = a

Aman has an equal number of one, five, ten and twenty rupee bank notes

$\Rightarrow$Â Total number of notes with Aman = 4a

Total amount with Aman = â‚¹ 1,080

$\Rightarrow$ Â $\left(1\times a\right)+\left(5\times a\right)+\left(10\times a\right)+\left(20\times a\right)=1080$

$\Rightarrow$ Â $36a=1080$

$\Rightarrow$ Â $a=30$

$\therefore\ $Total number of notes with Aman = 4a = 4 x 30 = 120

Hence, the correct answer is Option C

**Question 19:Â **Which two signs should be interchanged to make the given equation correct?

$(560\div80)+90\times8-38=600$

a)Â $+$ and $-$

b)Â $+$ and $\div$

c)Â $\div$ and $-$

d)Â $\times$ and $+$

**19)Â AnswerÂ (D)**

**Solution:**

By Trial and Error method,

__Option A__

$(560\div80)-90\times8+38=600$

$7-90\times8+38=600$

$7-720+38=600$

$-675=600$

Hence Option A is incorrect

__Option B__

$(560+80)\div90\times8-38=600$

$640\div90\times8-38=600$

$\frac{64}{9}\times8-38=600$

The value will be decimal after solving which is not possible

__Option C__

$(560-80)+90\times8\div38=600$

$480+90\times8\div38=600$

$480+720\div38=600$

$480+\frac{360}{19}=600$

The value will be decimal after solving which is not possible

__Option D
__

$(560\div80)\times90+8-38=600$

$7\times90+8-38=600$

$630+8-38=600$

$600=600$

Hence, the correct answer is Option D

**Question 20:Â **After giving a discount of 25% on the marked price, a laptop is sold at â‚¹ 22,500. What is its marked price?

a)Â â‚¹ 32,000

b)Â â‚¹ 36,500

c)Â â‚¹ 30,000

d)Â â‚¹ 29,000

**20)Â AnswerÂ (C)**

**Solution:**

Let the marked price be M

Discount = 25%

Selling price = â‚¹ 22,500

$\Rightarrow$Â $\frac{75}{100}\text{M}=22500$

$\Rightarrow$Â $\text{M}=30000$

$\therefore\ $Marked price =Â â‚¹ 30,000

Hence, the correct answer is Option C