1. In a 90 litres mixture of water and milk, the water is 30%. How many litres of water is required to increase the percentage of water in the mixture to 40%?
Ans:3 Milk :Water = 7:3 i.e quantity of water = 3/10 × 90 =27litres and quantity of milk = 63 Now required ratio is 6:4 i.e. 3:2 Quantity of milk =63 =3x/5 =>x= 105 litres i.e. required quantity of water = 42litres Increase = 42 – 27 =15 litres. Hence, option c.
2. Priya was married to Rajesh at the age of 24 years. Her present age is 4/3 times her age at the time of marriage. The present age of their son is 18.75% of the age of Priya at present. Rajesh is 29 years older to his son, then find the age of Rajesh at the time of his marriage.
Ans:4 Age of priya at present = 24 * (4/3) = 32 years Present age of their son = 18.75% of 32 = 6 years Present age of Rajesh = 6 + 29 = 35 years Since Rajesh got married before 8 years from present. So, age of Rajesh at the time of his marriage = 35 – 8 = 27 years
3. The base radii of two cylinders are in the ratio of 3:4 and their heights are in the ratio of 7:6. The ratio of their volume is
Ans:1 R1:R2=3:4H1:H2=7:6
Volume1/volume2=π(R1)2H/π(R2)2H=32*7/42*6=21:32
4. A shopkeeper sold 24 shirts at a profit of 20% and 16 shirts at a profit of 10%. If he had sold all the 40 shirts at a profit of 15%, then his profit would have been reduced by Rs. 36. What is the cost price of each shirt?
Ans:3 Let the cost price of each shirt be Rs. x, therefore, 24 × 1.2x + 16 × 1.1x – 40 × 1.15x = Rs. 36, solving we get x = Rs. 90. Hence, option c.
5. Raju bought a bike whose sale price was Rs. 50,000. He availed 30% discount on it under exchange offer and then 20% discount as credit card discount. Then he spent 15% of its sale price on its maintenance. At what price should he sell that bike to earn 15% profit?
Ans:1 Price = Rs. 50,000. After 30% discount, Price= Rs. 35000 After, 20% discount on this, Price = Rs. 28000 CP for Raju = Rs. 28000 +(15% of 50,000) = Rs. 35,500 SP = 1.15 * 35500 = Rs. 40825. Hence, option a.
6. A coaching center has increased the tuition fee by 30 % and simultaneously the number of students is decreased by 10%. What is the percentage change in the total amount collected by coaching centre?
Ans:2 Let the tuition fee be y and number of students be x. Total amount collected = xy Now, Tuition fee = x + 0.3x = 1.3x Number of students = y – 0.1y = 0.9y Total amount = 1.3x * 0.9y = 1.17xy Change =1.17xy – xy = 0.17xy i.e, 17% increase. Hence, option b.
7. P, Q and R started a business by investing ½, 1/3rd and 1/6th of the capital respectively. After 1/3rd of the total time, P withdrew his capital completely and after 1/4th of the total time Q withdrew his capital. R kept his capital for the full period. The ratio in which the total profit is to be divided amongst the partners is
Ans:3 Let X be the total investment for total time period Y P’s share = (X/2) * (Y/3) Q’s share = (X/3) * (Y/4) R’s share = (X/6) * Y Required ratio = 1/6 : 1/12 : 1/6 = 2:1:2
8. At what interest rate will a sum of money double itself in 3 years if the interest is compounded annually?
Ans:2 A = P (1+ r/100)TAs per the question, A = 2P
=> 2P = P (1 + r/100)3
⇒(1 + r/100)3 = 2
⇒1 + r/100 = 21/3
⇒ r/100 = 21/3 – 1 = 1.26 – 1 = 0.26
⇒ r = 26%
9. A bus covered a certain distance from village A to village B at the speed of 60 km/hr. However on its return journey it got stuck in traffic and covered the same distance at the speed of 40 km/hr and took 2 hours more to reach Its destination. What is the distance between village A and B?
Ans:1 Let the distance between A and B be ‘x’ km Let the time taken by bus while travelling from A to B be ‘t’ hours. Therefore, time taken by the bus from B to A is ‘t+2’ hours Time taken from A to B = t = x/60 Time taken from B to A = t + 2 = x/40 (x/60) + 2 = x/40 or x/120 = 2 or x = 240 km
10. A cistern has 3 pipes A, B and C. A and B can fill it in 3 hours and 4 hours respectively while C can empty the completely filled cistern in 1 hour. If the pipes are opened in order at 3, 4 and 5 p.m. respectively, at what time will the cistern be empty?
Ans:2 Pipe A can fill 1/3 rd of the cistern in 1 hour Pipe B can fill ¼ th of the cistern in 1 hour Pipe C can empty the cistern in 1 hour Pipe A is opened at 3 pm. By 4 pm, 1/3 rd of the tank is filled At 4 pm, pipe B is also opened. Hence, the fraction of cistern filled between 4 pm and 5 pm = 1/3 + 1/4 = 7/12 By 5 pm, portion of the cistern filled = 1/3 + 7/12 = 11/12 At 5 pm, pipe C is opened. From 5 pm, all 3 pipes will be open Portion of the cistern emptied in one hour when all 3 pipes are opened = 1 – 1/3 – 1/4 = (12 – 4 – 3)/12 = 5/12 Hence, to empty 11/12 th of the cistern, time taken = (11/12)/(5/12) = 2.2 hours Time taken to empty cistern = 2.2 hours i.e. 2 hours and 12 minutes Hence, at 7.12 pm, the cistern will be empty
dipanshu sahu