Q1. If length of each side of a rhombus PQRS is 8 cm and ∠PQR = 120°, then what is the length (in cm) of QS?
(a) 4√5
(b) 6
(c) 8
(d) 12
Directions (2-5): The table given below represents the production and sales of wheat in 4 different countries A, B, C and D over a period of 4 years. At the end of year 2010 A, B, C and D had a stock of 5200, 3500, 7835 and 1956 (in ‘000 quintals) of wheat respectively. For any given year, the stock of wheat is calculated as:
Q2. What is the surplus (in ‘000 quintals) of country A of years 2013 and 2014 taken together?
(a) 122
(b) 131
(c) 143
(d) 158
Q3. What is the stock (in ‘000 quintals) of country C at end of the 4 year period?
(a) 5926
(b) 6213
(c) 6826
(d) 8844
Q4. What is the difference (in ‘000 quintals) in average production and average sales of country C in the given four years?
(a) 252.25
(b) – 415.50
(c) 350.75
(d) 275.25
Q5. What can be said about total surplus of country B and country D over the 4 years?
(a) Surplus of B = Surplus of D
(b) Surplus of D > Surplus of B
(c) Surplus of B > Surplus of D
(d) No relation is there
Q6. By which least number should 5000 be divided so that it becomes a perfect square?
(a) 2
(b) 5
(c) 10
(d) 25
Q7. A can do a work in 8 days, B can do the same work in 10 days and C can do the same work in 12 days. If all three of them do the same work together and they are paid Rs 7400, then what is the share (in Rs) of B?
(a) 2600
(b) 3000
(c) 2400
(d) 2000
Q8. If the radius of the cylinder is increased by 25%, then by how much percent the height must be reduced, so that the volume of the cylinder remains same?
(a) 36
(b) 56
(c) 64
(d) 46
Q9. The marked price of an article is 20% more than its cost price. If 5% discount is given on the marked price, then what is the profit percentage?
(a) 5
(b) 14
(c) 15
(d) 25
Q10. If A : B = 2 : 5, B : C = 4 : 3 and C : D = 2 : 1, then what is value of A : C : D?
(a) 6 : 5 : 2
(b) 7 : 20 : 10
(c) 8 : 30 : 15
(d) 16 : 30 : 15
Solutions
S1. Ans.(c)
Sol.
⇒ Diagonals of a rhombus bisect each other at right angle
In ∆POQ, cos60°=OQ/PQ
⇒1/2=OQ/8⇒OQ=4
∴ QS = 2 × OQ = 4 × 2 = 8 cm
S2. Ans.(b)
Sol. Surplus of country A of year 2013 and 2014 taken together
= (1671 – 1641) + (1103 – 1002)
= 30 + 101 = 131 thousand quintal
S3. Ans.(c)
Sol. Stock of country C at end of 4 year period.
= [7835 + 2035 + 1821 + 1937 + 3014] –[2247 + 2018 + 2563 + 2988]
= 6826 thousand quintal
S4. Ans.(a)
Sol. Required difference
=|((2035+1821+1937+3014))/4–((2247+2018+2563+2988))/4|
=|8807/4–9816/4|
= |2201.75 – 2454| = 252.25 thousand quintal
S5. Ans.(b)
Sol. Surplus of country B over the 4 years
= (1881 – 1798) + (2067 – 2389) + (1328 – 2063) + (1578 –1239)
= 83 – 322 – 735 + 339 = –635
Surplus of country D over the 4 years.
= (3126 – 2417) + (2987 – 2917) + (2143 – 3188) + (4126 –3563)
= 709 + 70 – 1045 + 563 = 297
∴ surplus of D > surplus of B.
S6. Ans.(a)
Sol. When divided by 2 = 2500 (it is a perfect square of 50)
When divided by 5 = 1000 (it is not perfect square)
When divided by 10 = 500 (it is not a perfect square)
When divided by 25 = 200 (it is also not a perfect square)
S7. Ans.(c)
Sol. Ratio of time taken by them to do work
= 8 : 10 : 12 = 4 : 5 : 6
Ratio of efficiency=1/4 ∶1/5 ∶1/6 = 15 : 12 : 10
Since share is divided in the ratio of efficiency
So,share of B=7400/37×12 =Rs.2400
S8. Ans.(a)
Sol. Let initial radius = 4r
Increased radius = 5r
initial volume is πr² h₁ = π × 16 r² h₂
Find volume = π × 25 r² × h₂
π 16 r² × h₁ = π25 r² h₂ ⇒ h_1/h_2 =25/16
So height have to be decreased by
=9/25×100%=36%
S9. Ans.(b)
Sol. Let CP = 1000x ⇒ So, MP = 1200x
S.P.=95/100×1200x =1140
% profit=140x/1000x×100 =14%
S10. Ans.(d)
Sol. A : B : C : D = 16 : 40 : 30 : 15
A : C : D = 16 : 30 : 15
