IBPS Clerk Prelims: Quants Day 14

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1-5: There are four companies, namely AA, BB, CC, and DD. The following table shows the total cost and total sales of these companies for their different products.
For companies BB and DD, the ratio of sales to asset is same and equal to 3. However, sales of company BB is half that of company DD. Profit of company CC is 25% which is also equal to two-thirds of the profit of company AA.
Profit of company BB is same as that of company AA which amounts to 25% of BB sales. Cost of company DD is twice the sale of company CC.

1. What are the assets of DD company?
   A) Rs 37,500
   B) Rs 1,25,000
   C) Rs 1,00,000
   D) Rs 2,50,000
   E) None of these
   
   Answer & Explanation

   C) Rs 1,00,000
   Explanation:
   For the questions to be answered, first complete the table based on given information.
   Cost of CC is 1,00,000 and given that the profit % is 25%, so sales of CC = 125/100 * 1,00,000 = 1,25,000. This means profit of CC = 1,25,000 – 1,00,000 = 25,000
   Profit of CC is two-thirds of the profit of company AA, so profit of AA = 3/2 * 25,000 = 37500. Sales of AA = 1,00,000. So cost of AA = 1,00,000 – 37,500 = 62,500
   Profit of BB = Profit of AA = 37,500. Also, profit of BB = 25% of sales of BB. So, 37,500 = 25/100 * sales of BB. So, sales of BB = 1,50,000. This gives cost of BB = 1,50,000 – 37, 500 = 1,12, 500.
   Cost of DD is 2 times sales of CC. So, cost of DD = 2 * 1,25,000 = 2,50,000. Given sales of BB is half of DD. So, sales of DD = 2 * 1,50,000 = 3,00,000.
   And so on find remaining missing parts.
   *See the complete table in next Explanation
   
   
   
2. Find the ratio of profit to assets of company AA.
   A) 2 : 7
   B) 3 : 2
   C) 3 : 4
   D) 5 : 3
   E) None of these
   
   Answer & Explanation

   B) 3 : 2[table]

   	AA	BB	CC	DD
   Sales	1,00,000	1,50,000	1,25,000	3,00,000
   Cost	62,500	1,12,500	1,00,000	2,50,000
   Profit	37,500	37,500	25,000	50,000
   Assets	25,000	50,000	35,000	1,00,000

   [/table]
   

   
   
3. What is the cost of company CC?
   A) Rs 37,500
   B) Rs 1,25,000
   C) Rs 1,00,000
   D) Rs 2,50,000
   E) None of these
   
   Answer & Explanation

   C) Rs 1,00,000 Explanation:
   See the value from the table
   
   
4. What is the profit percentage of company DD?
   A) 20%
   B) 25%
   C) 28%
   D) 30%
   E) None of these
   
   Answer & Explanation

   A) 20%
   Explanation:
   Profit% = 3,00,000 – 2,50,000/2,50,000 * 100
   
   
5. What is the ratio of the profits of company CC to company DD?
   A) 1 : 3
   B) 2 : 1
   C) 1 : 2
   D) 6 : 5
   E) None of these
   
   Answer & Explanation

   C) 1 : 2
   Explanation:
   25,000 : 50,000
   
   
6. A completes a piece of work in 10 days, and B completes the same work in 18 days. Both A and B started the work, but A left after some days. Now B completed the remaining work in 6 4/5 days. Find the number of days after which A left?
   A) 2 days
   B) 3 days
   C) 4 days
   D) 5 days
   E) None of these
   
   Answer

   C) 4 days
   Explanation:
   Let A left after ‘x’ days. B completed remaining work in 6 4/5 days or 34/5 days. So,
   (1/10 + 1/18) * x + 1/18 * 34/5 = 1
   (1/10 + 1/18) * x = 1 – 17/45
   14/90 * x = 28/45
   Find x
   
   
7. A bottle contains a mixture of alcohol, acid and water in the ratio 1 : 2 : 3, while another bottle contains the same in the ratio 2 : 3 : 4. If both the solutions are mixed in the ratio 5 : 9, then the percentage of acid in the final solution is
   A) 33 1/3 %
   B) 33%
   C) 50%
   D) 28%
   E) None of these
   
   Answer & Explanation

   A) 33 1/3 %
   Explanation:
   Ratio of acid to alcohol+water in 1st solution = 2 : (1+3) = 1 : 2
   Ratio of acid to alcohol+water in 2nd solution = 3 : (2+4) = 1 : 2
   They are mixed in ratio 5 : 9
   So ratio of acid to alcohol+water in final solution = 1/3 * 5 + 1/3 * 9 : 2/3 * 5 + 2/3 * 9 = 1 : 2
   So, percentage of acid = 1/(1+2) * 100 = 100/3 %
   
   
   
8. Find out the number of words consisting of 3 consonants and 2 vowels out of 8 consonants and 3 vowels available.
   A) 1050
   B) 168
   C) 20160
   D) 25200
   E) None of these
   
   Answer & Explanation

   C) 20160
   Explanation:
   For consonants = 8C3 and for vowels = 3C2
   And for 5 words arrangement = 5!
   So total 8C3 * 3C2 * 5!
   
   
   
9. 10, 8, 13, 35, 135, 669, ?
   A) 1500
   B) 1890
   C) 3678
   D) 4007
   E) 4070
   
   Answer & Explanation

   D) 4007
   Explanation:
   10*1 – 2, 8*2 – 3, 13*3 – 4, 35*4 – 5,…., 669*6 – 7
   
   
   
10. x² = 1369; y = √1369
    A) x ≤ y
    B) x ≥ y
    C) x > y
    D) x < y
    E) No relationship
    
    Answer & Explanation

    A) x ≤ y
    Explanation:
    x² = 1369
    x = 37, -37
    y = √1369
    y = 37
    put on number line
    -37 37
    When y = 37, y ≥ x
    So y ≥ x