Sunday, 23 October 2016

Set A

1.A trader sells two articles, one at a loss of 10% and another at a profit of 15% but finally there is no loss or gain. If the total sale price of these two articles is Rs. 30, 000, find the difference between their cost prices:
(a) Rs. 5000
(b)Rs. 6000
(c) Rs. 7500
(d) None of these

2.60% goods are sold at 5% loss while rest are sold at 10% profit. If there is a total profit of Rs. 100, then the worth of goods sold it:
(a) Rs. 7500
(b) Rs. 5000
(c) Rs. 10000
(d) None of these

3.Two articles are sold at the same price. One at a profit of 75% and another one at  a loss of 30%. What is the overall profit or loss?
(a) 22.5% profit
(b) 57.5 profit
(c) 13 2/7 % loss
(d) None of these

4.Mr. Mittal purchased a car for Rs. 3, 00, 000 and a bike for his son for Rs. 1, 00, 000. He sold the car at a profit of 10% and bike at  a loss of 20%. What is the net gain or loss?
(a) 2% gain
(b) 1.5% loss
(c) 2.5 loss
(d) 2.5% gains

5.The profit percentage on the three articles A, B and C is 10% 20% and 25% and the ratio of the cost price is 1 : 2 : 4 . Also the ratio of number of articles sold of A, B and C is 2 : 5 : 2, then the overall profit percentage is:
(a) 18. 5%
(b) 21%
(c) 75%
(d) None of these

6.A single discount equivalent to three successive discounts of 5%, 10%, 20% is :
(a) 68. 4%
(b) 35%
(c) 31.6%
(d) 32%

7.On selling an article for Rs. 240, a trader loses 4%. In order to gain 10% he must sell that article for :
(a) Rs. 275
(b)Rs. 340
(c) Rs. 320
(d) Rs.264

8.6% more is gained by selling a coat for Rs. 1425 than by selling it for Rs. 1353. The cost price of the coat is :
(a) Rs. 1000
(b)Rs. 1250
(c) Rs.1500
(d)Rs. 1200

9.ITC sells one product at a profit of 20% another at a loss 20% at the same selling price. What is the loss incurred by ITC?
(a) 1 %
(b) 2 %
(c) 4%
(d) 0%

10.Each of A and B sold their article at Rs. 1818 but A incurred a loss of 10% while B gained by 1%. What is the ratio of cost price of the articles of A to that of B?
(a) 101 : 90
(b) 85 : 89
(c) 81 : 75
(d) None of these

ANSWERS AND SOLUTION :
1.(b)
10% x = 15% of y, where x + y = 30000
=> x/y = 3k/2k
Hence, the difference = k = 6000

2.(c)
SP of 60% goods=0.6y × 0.95=0.57y
} Total SP =1.01y
SP of 40% goods=0.4y × 1.1=0.44y
Profit = 0.01y = 100
y = 10000

3.(d)
4.(d)
Gain = 30000
Loss = 20000
Net gain = 10000 over Rs. 4 lakh
Hence, profit = 10000/400000 * 100 = 2.5%

5.(b)
CP of A + B + C = 2x * y + 5x * 2y + 2x + 4y = 20xy
Profit of A = 0.2xy
Profit of B = 2xy
Profit of C = 2xy
Total Profit = 4.2xy
% profit = 4.2xy/20xy * 100 = 21%

6.(c)
Reduced price = 100 * 0.95 * 0.90 * 0.80 = 68.40
so Single discount = (100 – 68.4)% = 31. 6%

7.(a)
Let the CP be Rs. x, then SP be 0.96x
so 0.96x = 240
X = 250
Now the new SP = 250 * 1.1 = 275

8.(d) 1435 – 1353 = 72 = 6% of CP
=> CP = 1200

9.(c)
Loss % = ((common gain or loss)/10)^2 %
= (20/10)^2 % = 4%

10.(a)
CP of A = 1818/0.9 = 2020
CP of B = 1818/1.01 = 1800
CP of A/CP of B = 2020/1800 = 101/90

Set B

1.Two equal sums were borrowed at 8% simple interest per annum for 2 years and 3 years respectively. The difference in the interest was Rs. 56/- The sums borrowed were:
(a) Rs. 800/-
(b) Rs. 700/-
(c) Rs. 560/-
(d) Rs. 350/-

2.A  CD was sold at a profit of 12 ½ %. If It had been sold at a profit of 15%, It would have gained him Rs. 10/- more. The cost price of CD is (in Rs.)
(a) 450
(b) 500
(c) 400
(d) 550

3.If 3x – 1/4y = 6, then the value of 4x – 1/3y is :
(a) 2
(b) 4
(c) 6
(d) 8

4.When two circle touch externally, the number of common tangents are :
(a) 4
(b) 3
(c) 2
(d) 1

5.Side BC of ABC is produced to D. If ∠ACD = 140° and ∠ABC = 3 ∠BAC, then find ∠A.
(a) 55°
(b) 45°
(c) 40°
(d) 35°

6.In a triangle, the angles are in the ratio 2 : 5 : 3. What is the value of the least angle in the radian?
(a) π/20
(b) π/10
(c)2π/5
(d) π/5

7.From 125 metre high towers, the angle of depression of a car is 45°. Then how far the car is from the tower?
(a) 125 metre
(b) 60 metre
(c) 75 metre
(d) 95 metre

8.A can do a piece of work in 6 days. B can do the same work in 12 days. How long would both of them take to do the same work?
(a) 2 days
(b) 4 days
(c) 6 days
(d) 8 days

9.The prize money of Rs. 1, 800/- is divided among 3 students A, B and C in such a way that 4 times the share of A is equal to 6 times the share of B, which is equal to 3 times the share of C. Then A’s share is :
(a) Rs. 400/-
(b) Rs. 600/-
(c) Rs. 760/-
(d) Rs. 800/-

10.On the eve of Gandhi Jayanti, Gandhi Ashram declared a 25% discount on silk. If selling price of a silk saree is Rs. 525/-. What is its marked price?
(a) Rs. 700/-
(b) Rs. 725/-
(c) Rs. 750/-
(d) Rs. 775/-

Answers with Explanation:-
1.(b); Let the borrowed = Rs. P
According to question, 56 = P * 8 * (3 – 2)/100
=> 5600/8 = P
=> P = Rs. 700/-

2.(c); Let cost price of CD = Rs. X
According to question,
X * 15/100 – x * 12 ½ * 1/100 = 10
=> 3x/20 – x/8 = 10
=> 6x – 5x/40 = 10
=> X = Rs. 400/-

3.(d); 3x – 1/4y = 6
4/3 (3x – 1/4y) = 4/3 * 6
(On multiplying by 4/3 both side)
4x – 1/3y =8

4.(b)
5.(d)
6.(d) Let first angle = 2x
Second angle = 5x
Third angle = 3x
2x + 5x + 3x = 180°
x = 18°
so Least angle =2x = 2 * 18°
= 36° = 36π/180° = π/5

7.(a)
8.(b) ; A’s 1 day work = 1/6
B’s 1 day work = 1/12
(A + B)’s 1 day work = 1/6 + 1/12 = 3/12 = 1/4
so Time taken by (A+B) = 4 days

9.(b) ; According to question,
A + B + C = 1800
A = 6B = 3C
A = 3B/2 and C = 2B
From equation (i),
3B/2 + B + 2B =1800 ⇒9B/2 = 1800 => B = Rs.400/-
so A = 3B/2 = 3/2 * 400 = Rs. 600/-

10.(a) Marked price = 525 * 100/(100 – 25)
= 525 * 4/3 = Rs. 700/-

Set C

1.A is  thrice efficient as B and C is twice as efficient as B. What is the ratio of number of days taken by A, B and C, when they work individually?
(a) 2 : 6 : 3
(b) 2 : 3 : 6
(c) 1 : 2 : 3
(d) 3 : 1 :  2
2.A and B can complete a task in 30 days when working together after A and B have been working together for 11 days. B is called away and A, all by himself completes the task in the next 28 days. Had A been working alone, the number of days taken by him to complete the task would have been:
(a) 33 3/19
(b) 19 6/25
(c) 44 4/19
(d) none of these

3.Sonu can do a piece of work in 20 days. He started the work and left after some days, when 25%  work was done. After it Abhijeet joined and completed it working for 10 days. In how many days Sonu and Abhijeet can do the complete work, working together?
(a) 6
(b) 8
(c) 10
(d) 12

4.Chandni and Divakar can do a piece of work in 9 days and 12 days respectively. If they work for a day alternatively, Chandni beginning, in how many days, the work will be completed?
(a) 10 ¼
(b) 9 1/5
(c) 11 : 11
(d) 10
5.Fatima and Zahira can do a piece of work in 12 days and 15 days respectively. If they work for alternate day and Fatima starts the work first, then in how many days the work will be completed?
(a) 12 1/5
(b) 13 1/4
(c) 13 1/5
(d) 15

6.A takes 6 days less than B to do a certain job and 2 days more than C. A and B together can do the work in the same time as C. In how many days B alone can do the complete work?
(a) 10
(b) 14
(c) 12
(d) 16

7.When A, B and C are deployed for a task, A and B  together do 70% of the work and B and C together do 50% of the work who is most efficient?
(a) A
(b) B
(c) C
(d) can’t be determined

8.A piece of work can be completed by 10 men and 6 women in 18 days. Men works 9 hours per day while women works 7. 5 hours per day. Per hour efficiency of a woman is 2/3rd of a man’s efficiency. In how many days 10 men and 9 women complete the work?
(a) 16 days
(b) 20 days
(c) 30 days
(d) 2 days

9.A can do a piece of work in 2 hours, B can do thrice the work in 8 hours and ‘C’ can do the same work as A in 8 hours . If all of them work together, how long it would take them to complete the work:
(a) 1 hour
(b) 2 hours
(c) 3 hours
(d) 4 hours

10.4 men and  2 boys can finish a piece of work in 5 days. 3 women and 4 boys can finish the same  work in 5 days. Also 2 men and 3 women can finish the same work in 5 days. In how many days 1 man, 1 woman and one boy can finish the work, at their double efficiency?
(a) 4  8/13
(b) 4 7/13
(c) 3  7/13
(d) none of these

ANSWERS AND SOLUTION :
1.(a)
2.(c)
Work done in 11 days = 11/30
Rest work = 19/30
1 day’s work of A = (19/30)/28 = 19/(30*28) = 19/840
Total number of days required to complete the whole work alone
= 1/(19/840) = 840/19 = 44 4/19days

3.(b)
Efficiency of Sonu = 5% = (100/20)
Rest work = 75%
so Efficiency of Abhijeet = 75/10 = 7.5%
so Combined efficiency of Sonu and Abhijeet
= 12. 5% = (7.5 + 5)
so Number of days required by Sonu and Abhijeet, to work together
= 100/12.5 = 8 days

4.(a)
5.(b)
6.(c)
Let B takes x days to complete the work individually,
Then, the B’s 1 day’s work = 1/x
A’s 1 day’s work = 1/(x -6)
C’s 1 day’s work = 1/(x – 8)
so 1/(x-6) + 1/x + 1/(x – 8)
Now either solve the equation or satisfy the equation from the choices given in the question.
Thus option (c) in correct.

7.(a)
8.(a)
Work of a man for 1 hour = 3/2 women’s work for 1 hour
again, work of a man for 1 day
= (3/2  ×9/7.5) women’s work for 1  hour
=>Work of a man for  1 day = 9/5 women’s work for 1 day
=>1 man = 9/5 women
so 10 men + 6 women =  10 * 9/5 + 6 = 24 women
so 10 men + 9 women = 10 * 9/5 + 9 = 27 women
Now,
D1 * W1 = D2 * W2
18 * 24 = D2 * 27
D2 = 16 days

9.(a)
10.(b)
Efficiency of 4 men and 2 boys = 20%
Efficiency of 3 women and 4 boys = 20%
Efficiency of 2 men and 3 women = 20%
so Efficiency of 6 men, 6 women and 6 boys = 60%
so Efficiency of 1 man, 1 women and 1 boy = 10%
Now, since they will work at double their efficiency
so Efficiency of1 man, 1 woman and 1 boy = 20%
so Required number of days = 5