Q1. Mr. Ravi spent 20% of his monthly income on food and 15% on children’s education, 40% of the remaining he spent on entertainment and transport together and 30% on medical. He is left with an amount Rs. 8775 after all these expenditures. What is Mr. Ravi’s monthly income?
(a) Rs. 40,000
(b) Rs. 35,000
(c) Rs. 45,000
(d) Rs. 38,000
Sol. let total monthly income of ravi =X
X of 30% of 65% = 8775 ⇒
=(8775 × 100 × 100)/(30 × 65)= Rs. 45,000
Q2. In a class of 35 students and 6 teachers, each student got toffees that are 20% of the total number of students and each teacher got toffees that are 40% of the total number of students. How many toffees were there?
Sol. 35 × 20% of 35 + 6 × 40% of 35
245 + 84 = 329
Q3. If the height of a cylinder is increased by 15% and the radius of its base is decreased by 10%, then by what percent will its curved surface area change?
(a) 3.5% decrease
(b) 3.5% increase
(c) 5% increase
(d) 5% decrease
Q4. A house and a shop were sold for Rs. 1 lakh each. In this transaction, the house sale resulted into 20% loss whereas the shop sale resulted into 20% profit. The entire transaction resulted in
(a) No loss no gain
(b) Gain of Rs. 1/24 lakh
(c) Loss of Rs. 1/12 lakh
(d) Loss of Rs. 1/18 lakh
Q5. A dishonest fruit seller sells fruits at 5% loss. If he uses 850 gm weight in place of 1 kg weight, then what is his profit percent?
BC is the chord of a circle with centre O. A is a point on major are BC as shown in the above figure. What is the value of ∠BAC + ∠OBC?
OB = OC
∴ ∠OBC= ∠OCB
∴ ∠OBC=90°- (∠BOC)/2
∴ ∠BAC+ ∠OBC=90°
Q8. N is the foot of the perpendicular from a point P of a circle with radius 7 cm, on a diameter AB of the circle. If the length of the chord PB is 12 cm, the distance of the point N from the point B is
(b) 75/7 cm
Q9. A square ABCD is inscribed in a circle of unit radius. Semi-circles are inscribed on each side as a diameter. The area of the region bounded by the four semi-circles and the circle is
(a) 1 sq unit
(b) 2 sq unit
(c) 1.5 sq unit
(d) 2.5 sq unit
Q10. A, B and C contract a work for 30,000. A and B complete (3/5)th of the work and then ‘C’ takes it over and finishes the work. How much does ‘C’ get?
Sol. Work done by A and B = 3/5
work done by C = 1-3/5 = 2/5
Amount paid to C = 30000*2/5 = 12000
Q11. A positive integer ‘a’ is a multiple of 5. If ‘a’ is divided by 4, the quotient and remainder are respectively q and 2. If 4q is divided by 5, the remainder is
Sol. Let the positive intiger a =5p
when 4q is dived by 5 remainder is -2 which is equal to 3(negative remainder theorem)
Q12. What is the maximum number of people who can share 24 five-rupee notes, 15 ten-rupee notes and 18 twenty-rupee notes equally?
Required number is
= HCF of 24,15 and 18
(a) 43 years
(b) 40 year
(c) 48 years
(d) 45 years
Sol. Let the present age of the father, mother and daughter be f, m and d respectively.
f + m + d = 105 …………………….. (1)
m + 15 = f + d
Substituting f + d as m + 15 in (1),
we get 2m + 15 = 105
2m = 90 =m = 45 years
Q14. The cost of three pens, four erasers and ten sharpeners is Rs. 75. The cost of six pens. Seven erasers and twenty sharpeners is Rs. 146. Find the cost of each eraser.
(a) Rs. 3
(b) Rs. 4
(c) Rs. 5
(d) Rs. 6
Sol. Let the cost of each pen, eraser and sharpener b p, e and s respectively.
3p + 4e + 10s = 75
6p + 7e + 20x = 146
Multiplying the first of the above equations by 2 and subtracting the second equation from it,
we get e = 4
Q15. Shyam and Ram have some chocolates with each of them, if shyam gives 5 chocolates of Ram, both will have equal number of chocolates. If Ram gives the same number of chocolates to shyam, shyam would have twice as many chocolates as Ram. Find the number of chocolates Ram has.
Sol. Let the number of chocolates with shyam and Ram be S and R respectively. If Shyam gives 5 chocolates to Ram, he would have S – 5 chocolates and Ram would have R + 5 chocolates.
So S – 5 = R + 5
S – R = 10 …………………… (1)
If Ram gives 5 chocolates to Shyam, he would have R – 5 chocolates and Shyam would have S + 5 chocolates.
S + 5 = 2 (R – 5)
2R – S = 15
Adding (1) and (2) we get R = 25.