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Numerical Ability Test - 2

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Numerical Ability Test - 2
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  • Question 1
    5 / -1
    The cost price of 8 tables is equal to the selling price of 5 tables. Find the percentage gain.
    Solution

    Given:

    CP of 8 tablets = SP of 5 tablets

    Formula:

    Profit = SP - CP

    Profit % = (SP - CP)/CP × 100

    Calculation:

    Let CP of one tablet be Rs.100.

    CP of 8 tablets = Rs.800 = SP of 5 tablets

    SP of one tablet = 800/5 = Rs.160

    ∴ Profit percentage = [(160 - 100)/100]× 100 = 60%

    Shortcut TrickCP of 8 tablets = SP of 5 tablets

    ⇒ CP/SP = 5/8

    SP > CP 

    Profit % = [(8 - 5)/5]× 100

    ⇒ 60%

    ∴ The percentage gain is 60%.

  • Question 2
    5 / -1
    A man sold 18 coats for Rs. 16,800, gaining thereby the cost price of 3 coats,. The cost price of a coat is:
    Solution

    Given:

    A man sold 18 costs for Rs. 16,800.

    Profit = Cost price of 3 cots.

    Calculations:

    S.P denotes selling Price and C.P denotes cost price.

    Now according to the question,

    (S.P. of 18 cots) – (C.P. of 18 cots) = (C.P. of 3 cots)

    C.P. of 21 cots = S.P. of 18 cots = Rs. 16800

    C.P. of 1 cot = Rs. (16800/21) = Rs. 800

    ∴ The cost price of a cot is Rs. 800.

  • Question 3
    5 / -1
    A man sells 30 apples for the cost price of 40 apples. His profit percentage (correct to two places of decimal) is :
    Solution

    Given:

    SP of 30 apples = CP of 40 apples

    Formula used:

    Profit = SP – CP

    Profit% = Profit/CP × 100

    Calculation:

    SP of 30 apples = CP of 40 apples

    ⇒ SP/CP = 4/3

    Profit = (4 – 3) = 1

    Profit% = (1/3 × 100)

    ⇒ 100/3%

    ⇒ 33.33%

    ∴ The profit percentage is 33.33%

  • Question 4
    5 / -1
    Which of the following is the single discount equivalent to successive discounts of 10% and 20%?
    Solution

    Given:

    The two discounts respectively = 10% and 20%

    Formula used:

    If a and b two successive discount then,

    Total discount = [a + b - (ab/100)]%

    Calculation:

    Let us assume the single discount be X

    ⇒ X = [10 + 20 - (10 × 20)/100]% = (30 - 2)% = 28%

    ∴ The required result will be 28%.

  • Question 5
    5 / -1
    An article was sold at 65% of its marked price, and thus there was a gain of 30%. Find the ratio of the marked price to cost price.
    Solution

    Given:

    An article was sold at 65% of its marked price

    There was a gain = 30%

    Calculation:

    Let the Cost price be 100 and Marked price be x

    According to the question

    An article was sold at 65% of its marked price = (65% of x)

    And there was a gain = (130% of 100)

    Now,

    ⇒ (65/100 × x) = (130/100 × 100)

    ⇒ 13x/20 = 130

    ⇒ 13x = (130 × 20)

    ⇒ x = (130 × 20)/13

    ⇒ x = 200

    Now,

    The ratio of the marked price to cost price = (200 : 100)

    ⇒ 2 : 1

    ∴ The required ratio is 2 : 1

  • Question 6
    5 / -1
    Vinay sold a watch at Rs.75 he gets profit as the same as cost price of the watch, then cost price of the watch is:
    Solution

    Concept:

    Profit = S.P. - C.P. 

    Calculation:

    S.P. = Rs.75

    Let C.P. be Rs.x.

    ⇒ Profit = C.P. = x

    We know that,

    Profit = S.P. - C.P. 

    ⇒ x = 75 - x

    ⇒ 2x = 75

    ⇒ x = 37.5

    Hence, the cost price of the watch is Rs.37.5.

    Confusion Points Here, in the question, absolute profit is given and not the profit percentage. So, it means that the profit value and the cost price would be actually equal.

    As we know,

    SP = CP + Profit

    SP = CP + CP = 2 CP (As it is given that profit is equal to the CP.)

  • Question 7
    5 / -1

    Vishnu and Deepak is two business partners. Vishnu invests Rs. 50,000 for 8 months and Deepak invests Rs. 20,000 for 10 months. Find the share of Vishnu from the total profit of Rs. 60,000.

    Solution

    Given:

    Vishnu Invests (I1) = Rs.50000

    Time (t1) = 8 months

    Deepak Invests (I2) = Rs.20000

    Time (t2) = 10 months

    Total profit = Rs.60000

    Formula:

    Profit = Investments × time

    Profit (P1)/Profit (P2) = (I1/I2) × (t1/t2)

    Calculation:

    We know that –

    Profit (P1)/Profit (P2) = (I1/I2) × (t1/t2) …….. (1)

    Put all the given values in equation (1) then we get

    (P1/P2) = (50000/20000) × (8/10)

    ⇒ (5/2) × (8/10)

    ⇒ 40/20

    ⇒ 2/1

    Now,

    Profit shares of Vishnu = (2/3) × 60000

    ⇒ 2 × 20000

    ⇒ 40000

    ∴ The Profit shares of Vishnu will be Rs. 40,000
  • Question 8
    5 / -1
    Mohan purchased a car of Rs. 8000 and sold it after one year at a loss of 25%. Find the selling price of car:
    Solution

    Given:

    Cost price of car = Rs. 8000

    Loss % = 25%

    Formula used:

    Selling price = Cost price - Loss

    Calculation:

    According to the question,

    Loss = Loss % of C.P

    ⇒ Loss = 8000 × 25/100 = 2000

    Now,

    Selling price = Cost price - Loss

    ⇒ Selling price = 8000 - 2000 = Rs. 6000

    ∴ The selling price of car is Rs. 6000.

  • Question 9
    5 / -1
    A grocer buys wheat at Rs. 3600 per quintal. At what rate per kg. must he sell to gain 20%.
    Solution

    Given:

    Cost price = Rs. 3600/quintal

    Concept used:

    1 Quintal = 100 Kg

    Formula used:

    Cost price(CP) + Profit = Selling price(SP)

    Profit% = (Profit/CP) × 100

    Calculation:

    CP = 3600/quintal = 36/kg

    Profit = 0.2CP

    SP = CP + Profit

    ⇒ SP = 1.2CP

    ⇒ 36 × 1.2 = 43.2

    ∴ He must sell them at Rs . 43.2/kg

  • Question 10
    5 / -1
    Rakesh sold a car for Rs.5,00,000 at a 28% profit. At what price should he sell it to get a 32% profit?
    Solution

    Given: 

    Selling Price of the car = Rs.500000

    Profit = 28% 

    Formula used:

    Selling Price percent  = (Cost Price + Profit) percent 

    Calculation:

    Profit is calculated on the cost price of the car and the cost price 100% of itself. 

    Selling Price percent  = (Cost Price + Profit) percent 

    ⇒ 128% = 100% + 28% 

    If 128% of the Cost Price = Rs.500000

    ⇒ 100% of the Cost Price = Rs.500000/128 × 100 

    ⇒ 100% of the Cost Price = Rs.390625

    ⇒ 132% of the Cost Price = Rs.390625 × 132/100

    ⇒ Rs.515625

    ∴ Rakesh should sell his car for Rs.515625 to get a 32% profit. 

    Alternate MethodProfit is 28%.

    128% of CP = 500000

    ⇒ 1% = 500000/128

    32% profit means 132% of CP.

    132% = 132 × (500000/128)

    ⇒ Rs. 515625

    ∴ Rakesh should sell his car for Rs.515625 to get a 32% profit. 

    Shortcut TrickSelling Price at 32% profit. 

    ⇒ Rs.500000 × 132/128 = Rs.515625

     

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