MAT (Stage-1) Mock Test

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MAT (Stage-1) Mock Test - 56

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Question 1
1 / -0

A group of 60 men can complete a piece of work in a certain number of days. If 10 more men join them, then the work can be completed in 8 days less. How many days will be required to complete the same work by 100 men?

A

B

C

D

Solution

Let the amount of work done by 1 man in 1 day be w.
Let the total number of days taken initially to complete the work be d.
Let the amount of total work be W.
So, 60dw = W ...(i)
Now, when 70 men do the work, it takes 8 days less.
So, 70w(d - 8) = W ...(ii)
Equating (i) and (ii), we get:
60d = 70(d - 8)
d = 56
So, W = w × 60 × 56
Now, let 100 men take D days to complete the work.
So, 100 × D × w = W = w × 60 × 56
Question 2
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A alone can finish a piece of work in 10 days and B alone can finish it in 15 days. If they work together and finish it, then out of the total wage of Rs. 75, A will get _________.

A
Rs. 30

B
Rs. 37.50

C
Rs. 45

D
Rs. 50.50

Solution

Ratio of efficiency of A and B = 3 : 2
A will get 3th/5 of the wage = Rs. 3/5× 75 = Rs. 45
Question 3
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The ratio between the ages of A and his father is 1 : 7. The difference between their ages is 30 years. What would be the ratio of their ages 10 years later?

A
9 : 33

B
4 : 13

C
3 : 1

D
1 : 3

Solution

Let the ages of A and his father be x and 7x respectively.
So, 7x - x = 30
x = 5 years
Present age of A = 5 years
Present age of A's father = 7 × 5 = 35 years
So, 10 years later, the ratio would be as follows.
(5 + 10) : (35 + 10)
= 15 : 45 = 1 : 3
Question 4
1 / -0

The present ages of Samir and Tanuj are in the ratio of 8 : 15. After 9 years, the ratio of their ages will be 11 : 18. What is the difference between their present ages?

A
21 years

B
28 years

C
35 years

D
22 years

Solution

Let the present ages of Samir and Tanuj be 8x and 15x respectively.
According to the question, after 9 years,

144x + 162 = 165x + 99
165x - 144x = 162 - 99
21x = 63
x = 3
Samir's present age = 8 × 3 = 24 years
Tanuj's present age = 15 × 3 = 45 years
Required difference = 45 - 24 = 21 years
Question 5
1 / -0

The ratio of the present ages of Sunita and Vinita is 4 : 5. Six years hence the ratio of their ages will be 14 : 17. What will be the ratio of their ages 12 years from now?

A
4 : 5

B
17 : 19

C
16 : 19

D
11 : 14

Solution

Let the present ages of Sunita and Vinita be 4x and 5x respectively.
Six years hence,

Or 68x + 102 = 70x + 84
2x = 18, x = 9
So, the ratio of the ages of Sunita and Vinita after 12 years will be,
4x + 12 : 5x + 12
= 36 + 12 : 45 + 12
= 48 : 57
= 16 : 19
Question 6
1 / -0

The average age of a class of 30 students and a teacher reduces by 0.5 years if we exclude the age of the teacher. If the initial average was 14 years, then find the age of the teacher.

A
26 years

B
32 years

C
29 years

D
28 years

Solution

Average age of 30 students and 1 teacher = 14 years
Total age of 31 persons = 31 × 14 years = 434 years
Average age of 30 students = (14 - 0.5) years = 13.5 years
Total age of 30 students = 30 × 13.5 years = 405 years
Thus, the age of the teacher = (434 - 405) years = 29 years
Question 7
1 / -0

When a number 'a' is first increased by 30% and then reduced by 30, the result obtained is 230. If the same number 'a' is first reduced by 30% and then increased by 30, then find the resultant value.

A
200

B
170

C
150

D
120

Solution

Let the required number be X.
The resultant number is 230.
We will add 30 to get the number before deduction as follows.
230 + 30 = 260
260 is 130% of X.
So, the required number will be, 260/130 × 100= 200
Now, after deducting 30% we get,= 200 - 60 = 140
The number is increased by 30.
So, 140 + 30 = 170.
Hence, the required number is 170.
Question 8
1 / -0

If the profit earned by selling 4 dozen eggs is equal to the cost price of a dozen eggs, then find the profit percentage.

A
20%

B
25%

C
30%

D
35%

Solution

Let the cost price of a dozen eggs be Rs. 12.
So, the price of 4 dozen eggs is 48.
So, the profit will be, 12/48 × 100 = 25%
Question 9
1 / -0

The difference between the compound interest and the simple interest on a certain sum for 2 years at 10% per annum is Rs. 10. Find the sum.

A
Rs. 1500

B
Rs. 1200

C
Rs. 1000

D
Rs. 700

Solution

Difference between the compound interest and the simple interest = C.I. - S.I. = for 2 years .
Given that, C.I. - S.I. = 10
Question 10
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A person spends 50% of his monthly salary on rent (R), 5% of the remaining salary on food (F), 10% of the remaining salary on transport (T) and 20% of the remaining salary on various bills (B). If his monthly salary is Rs. 20000, then what will be the descending order of the amounts spent on various items?

A
R, T, F, B

B
R, F, T, B

C
R, T, B, F

D
R, B, T, F

Solution

Total monthly salary = Rs. 20,000
Rent (R) = 50% = Rs. 10,000
Food (F) = 5% of 10,000 = Rs. 500 [∴ Remaining salary = Rs. 9500]
Now, transport (T) = 10% of Rs. 9500 = Rs. 950 [∴ Remaining salary = Rs. 8550]
Bills (B) = 20% of Rs. 8550 = Rs. 1710 [∴ Remaining salary = Rs. 6840]
∴ Correct order (decreasing amounts) = R, B, T, F
Question 11
1 / -0

If the selling price of 30 pens is equal to the cost price of 20 pens, then what is the net profit or loss percentage?

A
20% profit

B
20% loss

C

D

Solution

Let the C.P. per pen be Re. 1.
C.P. of 20 pens = Rs. 20
S.P. of 30 pens = Rs. 20
Question 12
1 / -0

The population of a village is 32,800. One-fourth of the population are females and the rest are males. 15% of the males and 35% of the females are uneducated. What percent on the whole are educated?

A
70%

B
80%

C
90%

D
60%

Solution

Number of males = 32,800 × 3/4 = 24,600

Number of females = 32,800 - 24,600 = 8200

Number of educated males = 24,600 × 85/100 = 20,910

Number of educated females = 8200×65 / 100 = 5330

Total number of educated persons = 26,240

Required percentage = 26,240 / 32,800 × 100 = 80%
Question 13
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Two trains start from stations A and B respectively, 50 km apart, at the same time and same speed. As the trains start, a bird flies from one train towards the other and on reaching the second train, it flies back to the first train. It repeats this process till both the trains collide. If the speed of both the trains is 25 km/hr and that of the bird is 100 km/hr, then how much did the bird travel till the time of collision? (Also consider that both the trains are moving on the same track.)

A
98.75 km

B
100 km

C
95.5 km

D
None of these

Solution

The collision will take place after 1 hour (Distance/Relative speed of the trains or 50/50).
The bird travels for 1 hour before the collision took place.
In 1 hour, it will travel 100 km, as its speed is 100 km/hr.
Question 14
1 / -0

If + means -, × means ÷, ÷ means × and - means +, then 445 × 5 - 31 ÷ 4 + 7 is equal to ________.

A
207

B
208

C
206

D
210

Solution

445 × 5 - 31 ÷ 4 + 7
After interchanging the signs, we get
445 ÷ 5 + 31 × 4 - 7
= 89 + 31 × 4 - 7
= 89 + 124 - 7
= 213 - 7 = 206
Question 15
1 / -0

If - means ×, × means ÷, ÷ means + and + means -, then 9 ÷ 128 × 8 + 1 - 3 is equal to _______.

A
20

B
21

C
10

D
22

Solution

9 ÷ 128 × 8 + 1 - 3
After interchanging the signs, we get
= 9 + 128 ÷ 8 - 1 × 3
= 9 + 16 - 3 = 22