### LR-ARITHMETICAL REASONING PROBLEMS:

**Q(1) A bus driver knows four different routes from Delhi to Bareli, he knows three different routes from Bareli to Lucknow and two different routes from Lucknow to Gorakhpur. How many different routes he knows from Delhi to Gorakhpur ?**

(a) 24 routes (b) 12 routes (c) 20 routes (d) 8 routes (e) None of these

Solution:- Total number of routes from Delhi to Gorakhpur= 4×3×2=24

**Q(2) Krishna was to earn Rs 4000 and a free holiday for eight weeks work. He worked for only 3 weeks an earned and Rs. 1200 and a free holiday. what was the value of holiday ?**

(a) 260 (b) 358 (c) 480 (d) 440 (e) None of these

Solution:-Let the cost of holiday was Rs x then,

Pay for 8 weeks work = 4000 + x

Pay for 8 Weeks Work = 4000+x/8

3 *(4000+x/8)=1200 + x

x= 480, option c is correct

**Q(3) The diagram given below, In this 400 candidates appeared in an examination. The diagram gives the number f students who failed in subjects Maths, English and Science. What is the percentage of students who failed in at least two subjects ?**

Solution :- Number of students who failed in at least two subjects = number of students who failed in two or more subjects = 12 + 8 + 8 + 6 = 34

Required % = (34/400)*100 = 8.5%

**Q(4) Ram has some mangoes to distributes among his students. If he keep 4, 5, 6 in a pack he left with one mango, But if he keeps 11 mangoes in a pack left with no mangoes. What is the minimum number of mangoes he has to distribute ?**

(a) 141 (b) 100 (c) 121 (d) 151 (e) None of these

Solution :-The required number will be such that it will produce a remainder 1 when divided by 4, 5 and 6 but gives no remainder when divided by 11, So, the required number of mangoes will be 121, option (c) is correct.

**Q(5) In a school, 65 % students plays cricket, 40 % plays football and 25 % plays both foolball and cricket. What percentage of students neither plays cricket nor plays football ?**

(a) 10 (b) 5 (c) 20 (d) 15

Solution:-Let the total number of students are 100

Let Cricket represents C, Football as F Then

C + 25 = 65, ∴ C=40

F + 25 = 40, ∴ F = 15

∴ Number of students neighter plays cricket nor plays football = 100 - ( C + F + 25 ) = 20 % , Option (c) is correct

**Q(6) Three quantities A, B and C are such that AB = KC, where K is a constant. When A is kept constant, B varies directly as C, When B is kept constant , A varies directly C and when C is kept constant, A varies inversely as B. Initially , A was at 5 and A : B : C was 1 : 3 : 5. Find the value of A when B equals 9 at constant C.**

(a) 8.33 (b) 8 (c) 9.25 (d) 9.55

Solution :- Initially when A : B : C = 1 : 3 : 5 and A = 5, then B = 15 and C = 25

AB = KC (given), So, 5 × 15 = K × 25

So K = 3, Now equation becomes AB = 3C

When B = 9 at constant C, A × 9 = 3 × 25

A = 8.33 option A is correct.

**Q(7) A car travels from A to B at V1 km/hr, travels back from B to A at V2 km/hr and again goes back from A to B at V2 km/hr. The average speed of the car is :**

Solution :- Let the distance between two cities be A Km, Then average speed:

Option (c) is correct

**Q(8) A, B, C, D and E play a game of cards. A says to B " If you give me 3 cards, you will have as I have at this moment while if D takes 5 cards from you, he will have as many as E has ". A and C together have twice as many cards as E has. B and D together also have the same number of cards as A and C taken together . If together they have 150 cards. How many cards C has ?**

(a) 22 (b) 24 (c) 26 (d) 28 (e) 30 ( asked in CAT )

Solution :- Here , A + B + C + D + E = 150

A = B - 3

A + C = 2E

D + 5 = E

B + D = A + C = 2 E

2 E + 2 E + E = 150, E = 30

D + 5 = 30 , D = 25

B + 25 = 2 × 30 B = 35

A = 35 - 3 = 32

32 + C = 2 × 30 C = 28 option ( d ) is correct