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MAT (Stage-1) Mock Test - 30

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MAT (Stage-1) Mock Test - 30
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  • Question 1
    1 / -0

    A man buys a scooter for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the scooter?

    Solution

    Cost price = Rs. 1400
    SP = CP - Loss % of CP
    Selling price = 1400 - 15% of 1400 = Rs. 1190

     

  • Question 2
    1 / -0

    How much time will it take for an amount of Rs. 900 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

    Solution

    Principal = P = Rs. 900 and SI = Rs. 81
    Time = ? and rate = 4.5%
    Time = (100 × SI)/( P × R)
    = (100 × 81)/( 900 × 4.5) = 2 years
    Required time = 2 years

     

  • Question 3
    1 / -0

    A sum of money placed at compound interest doubles itself in 4 years. In how many years will it amount to 8 times?

    Solution

    Let Principal = Rs. 100
    Amount = Rs. 200
    Rate = r%
    Time = 4 years
    Now,
    A = P × [1 + (r/100)]n
    200 = 100 × [1 + (r/100)]4
    2 = [1 + (r/100)]4 ... (i)
    If sum becomes 8 times in the time n years, then
    8 = [1 + (r/100)]n
    23 = [1 + (r/100)]n ... (ii)
    Comparing equations (i) and (ii), we get
    [1 + (r/100)4]3 = [1 + (r/100)]n
    [1 + (r/100)]12 = [1 + (r/100)]n
    Thus, n = 12

     

  • Question 4
    1 / -0

    Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds?

    Solution

    We know, total distance = 200 km
    If both the trains crossed each other at a distance of 110 km, then one train covered 110 km and the other 90 km [110 + 90 = 200 km].
    So, ratio of their speeds = 110 : 90
    = 11 : 9

     

  • Question 5
    1 / -0

    If I try to distribute some marbles equally among 6, 7, or 8 kids, I am left with the same number of marbles in each case of distribution. However, I can equally distribute them among 13 kids. What can be the minimum number of marbles that I may have with me?

    Solution

    Since the marbles can be distributed among 6, 7 and 8 kids leaving same number of leftover marbles in each case, let's find the LCM of 6, 7 and 8 = 168
    Possible remainders can be 1, 2, 3, 4 and 5.
    Suppose, I was left with 1 marble.
    That means total marbles = 168 + 1 = 169
    This is completely divisible by 13 as 169 is a multiple of 13.
    No other remainder possibility satisfies the divisibility rule of 13.
    Thus, total number of marbles = 169

     

  • Question 6
    1 / -0

    How many numbers less than 10,000 are divisible by each of the numbers 21, 36 and 66?

    Solution

    LCM of 21, 36, 66 = 2772
    Multiples of 2772 less than 10000 are: 2772, 5544 and 8316.

     

  • Question 7
    1 / -0

    The average daily wage of 8 men, 10 women and 2 girls is Rs. 280. If the average daily wage of the men is Rs. 10 more than that of the women and the average daily wage of the women is Rs. 10 more than that of the girls, then the average daily wage of the men is

    Solution

    Total daily wages = 280 × 20 = Rs. 5600
    Let average daily wage of girls be Rs. x.
    Average daily wage of women = Rs. (x + 10)
    Average daily wage of men = Rs. (x + 20)
    According to the given condition,
    8(x + 20) + 10(x + 10) + 2x = 5600
    20x = 5340
    x = Rs. 267
    Hence, average daily wage of men = Rs. (x + 20) = Rs. 287

     

  • Question 8
    1 / -0

    The average daily expenditure of Abha, Arya and Disha is Rs. 2000. If the average daily expenditure of Abha is Rs. 100 more than that of Arya and the average daily expenditure of Arya is Rs. 200 more than that of Disha, then the average daily expenditure of Abha is

    Solution

    otal expenditure = 2000 × 3 = 6000
    Let average daily expenditure of Disha be Rs. x.
    Average daily expenditure of Arya = Rs. (x + 200)
    Average daily expenditure of Abha = Rs. (x + 300)
    According to the given condition,
    x + (x + 200) + (x + 300) = 6000
    3x = 5500
    x = Rs. 1833.3
    Hence, average daily expenditure of Abha = 1833.3 + 300 = Rs. 2133.3 ~ Rs. 2133

     

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