MAT (Stage-1) Mock Test

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MAT (Stage-1) Mock Test - 49

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following numbers will replace the question mark (?) in the figure given below?

A
16

B
144

C
18

D
30

Solution
Question 2
1 / -0

The average price of three items of furniture is Rs. 21,000. If their prices are in the ratio 5 : 7 : 9, then the price of the costliest item is

A
Rs. 15,000

B
Rs. 21,000

C
Rs. 27,000

D
Rs. 28,900

Solution

Let the price of the 1st item be 5x, that of the 2nd item be 7x and that of the 3rd item be 9x.

x = 3000

Hence, price of the costliest item = 9 × 3000 = Rs. 27,000
Question 3
1 / -0

The average score of a cricketer in a certain number of innings is 15. When he scores a duck in the next innings, his average drops to 13.5. How many innings has he played, including the latest one?

A
12

B
10

C
11

D
9

Solution

Let the number of innings initially played by the cricketer be x.
Total runs scored by the cricketer = 15x
New number of innings = x + 1

15x = 13.5x + 13.5
⇒ 1.5x = 13.5
⇒ x = 9
Number of innings played, including the latest one = 9 + 1 = 10
Question 4
1 / -0

A obtained scores of 78, 93, 82 and 76 in four Maths exams. What is the minimum score A should obtain in the next Maths exam, so that he has an average of at least 85 in the five exams?

A
96

B
98

C
92

D
90

Solution

Total of scores obtained in 4 exams = 78 + 93 + 82 + 76 = 329

∴ Total marks to be obtained to get an average of at least 85 in 5 exams = 85 × 5 = 425

Minimum score required in the 5th exam = 425 - 329 = 96
Question 5
1 / -0

Sharad covers two-thirds of a certain distance at 4 km/hr and the remaining at 5 km/hr. If he takes 42 minutes in all, then the distance is

A
2.5 km

B
4.6 km

C
4 km

D
3 km

Solution

Let the distance be x km.
Question 6
1 / -0

Five bells begin to toll together and toll individually at the intervals of 6, 5, 7, 10 and 12 seconds. How many times will they toll together in one hour, excluding the one at the start?

A
7 times

B
8 times

C
9 times

D
11 times

Solution

LCM (6, 5, 7, 10, 12) = 420 sec = 7 min

So, the bells will toll together after every 7 minutes.

60 min ÷ 7 min = 8 (plus 4 remainder)

So, in the duration of 1 hour, they will toll together 8 times.
Question 7
1 / -0

There are two numbers. If 80% of the first number is added to the second number, then the resultant number is equal to 250% of the first number. What will be the ratio of the first to the second number?

A
10 : 17

B
10 : 16

C
17 : 10

D
10 : 7

Solution

Let the first and second numbers be x and y, respectively.
According to the question,
⇒ (80% of x) + y = 250% of x
⇒ 170% of x = y
⇒ 170x = 100y
Question 8
1 / -0

A man has divided his total money in his will in such a way that half of it goes to his wife, 2^rd/3 of the remaining amount to his two sons equally and the rest among his four daughters equally. If each daughter gets Rs. 25,000, then how much money will each son get?

A
Rs. 1,00,000

B
Rs. 75,000

C
Rs. 6,50,000

D
Rs. 50,000

Solution

If each daughter gets Rs. 25,000, four daughters get Rs. 1,00,000. Money shared with sons was double than that of daughters i.e. Rs. 2,00,000.

Share of each son = 2,00,000 ÷ 2 = Rs. 1,00,000
Question 9
1 / -0

Sherlock gave 30% of his income to his elder son, 40% of the remaining to the younger son and 25% of the balance is donated to an orphanage home. He was left with Rs. 11,340. His income was

A
Rs. 36,000

B
Rs. 40,000

C
Rs. 32,000

D
Rs. 30,000

Solution

Let the total income be 'S'.

Amount left after giving 30% to elder son = 70% of S = 0.7S

Amount left after giving 40% of remaining amount to younger son = 60% of 0.7S = 0.42S

Amount left after giving 25% of remaining amount to orphanage home = 75% of 0.42S = 0.315S

So, 0.315S = 11,340
Question 10
1 / -0

A can build a wall in 8 days, while B can break it in 3 days. A works for 4 days, then B joins to work with A for another 2 days. In how many days will A alone build up the remaining part of the wall?

A

B

C

D

Solution

A can build the wall in 8 days.
B can break the wall in 3 days.
According to the question,

,where x = Number of days in which A alone builds up the remaining part of the wall
Question 11
1 / -0

A and B together can do a piece of work in 80 days. B and C can do it in 120 days. On the first day, only A and B worked together and on the second day, only B and C worked together. For the following days, B worked for all the days, but A and C worked on alternate days only. How long did the work last?

A
88 days

B
90 days

C
96 days

D
98 days

Solution

Let the work done by A in a day be A.

Let the work done by B in a day be B.

Let the work done by C in a day be C.

Total work = W

Suppose, total work is completed in 2d days.

According to the question,

⇒ 5d = 240

⇒ d = 48 days

Number of days required to finish the work = 2d = 2 × 48 = 96 days
Question 12
1 / -0

Three taps together can empty a tank in 3 hours. The first tap alone and the second tap alone can empty it in 6 hours and 9 hours, respectively. How many hours will it take for the third tap alone to empty the tank?

A
12 hours

B
15 hours

C
18 hours

D
20 hours

Solution

Time taken by the first tap alone to empty the tank = 6 hours
Time taken by the second tap alone to empty the tank = 9 hours
Let the time taken by the third tap alone be 't' hours.
Now, according to the question,
Question 13
1 / -0

If Jatin walks from his house to school at the rate of 6 km/hr, then he reaches school 12 minutes earlier than the scheduled time. However, if he walks at the rate of 4 km/h, then he reaches 13 minutes late. Find the distance of his school from his house.

A
5 km

B
6 km

C
7 km

D
8 km

Solution

According to the question, distance between his house to school = (Difference of time in minutes)/60

(Where S1 is the speed at which Jatin reaches school earlier than the scheduled time and S2 is the speed at which Jatin reaches school later than the scheduled time)
Question 14
1 / -0

A motorboat in still water travels at a speed of 48 km/h. It goes 63 km upstream in 1 hour 30 minutes. The time taken by it to cover the same distance down the stream will be

A
1 hour 8 minutes

B
1 hour 22 minutes

C
1 hour 10 minutes

D
1 hour 20 minutes

Solution

Speed of the motorboat in still water, x = 48 km/h
Speed of the water = y km/h
Question 15
1 / -0

A man takes a loan of Rs. 4000 at SI rate of 5% per annum. After what time will he have to pay Rs. 4600 to clear the debt?

A
3 years

B
5 years

C
2 years

D
10 years

Solution

P = Rs. 4000
R = 5%
T = ?
A = Rs. 4600
SI = Rs. 600