This is class 10 mathematics MCQ/ multiple choice questions from the first part of Mathematics. This is mathematics multiple choice questions/ objective questions with solutions of Tax and Money Exchange, Successive Discount, Compound Interest, Population Growth and Depreciation chapters.
MULTIPLE CHOICE QUESTIONS
1. If the discount amount given in an item is 25% of its selling price, then the actual rate of discount is
a) 16$\frac{2}{3}$%
b) 20%
c) 25%
d) 30%
2. A stationer allows equal rate of discount in each item. If a customer pays Rs. 405 for a book printing Rs 450 on it, at what price can a student buy the pen costing Rs 50 in the same shop?
a) Rs 45
b) Rs 50
c) Rs 55
d) Rs 40
3. If the sales tax is 10% of marked price, what is actual sale tax rate?
a) 11$\frac{1}{9}$%
b) 9$\frac{1}{11}$%
c) 11$\frac{1}{3}$%
d) 9$\frac{10}{11}$%
4. The advertised price of a television is x, what will be its selling price after deduction of two successive discounts at the rates of y% and z%?
a) $x \left ( 1- \frac{y+z}{100} \right )$
b) $x \left (1- \frac{y+z}{100} \right )$
c) $x \left (1- \frac{y}{100} \right ) \left (1-\frac{x}{100} \right )$
d) $x \left (1+ \frac{y-z}{100} \right ) $
5. What will be the cost of a bag costing Rs 1800 after levying 13% VAT?
a) Rs 2043
b) Rs 2034
c) Rs 2340
d) Rs 3420
6. In a shopping complex 5% discount is given in every item. On the occasion of New Year, if it announces next 5% cash back as discount, how much should a customer pay for a refrigerator with its catalog price Rs 20000?
a) Rs 18000
b) Rs 22000
c) Rs 18005
d) Rs 18050
7. The marked price of a jacket is Rs 2500. If the shopkeeper allows certain discount and sells it for Rs 2260 with 13% value added tax, what is the rate of discount?
a) 20%
b) 15%
c) 13%
d) 10%
8. The price of a mobile excluding and including value added tax are Rs 4950 and Rs 5445 respectively. If the rate of discount is same as that of value added tax then its marked price is
a) Rs 4000
b) Rs 4400
c) Rs 5500
d) Rs 5445
9. A tourist bought a Nepali art with 13% VAT. If he got back Rs 520 at airport while leaving Nepal, what was the actual price of the art?
a) Rs 3000
b) Rs 4000
c) Rs 5000
d) Rs 6000
10. If 1£ = NRs 119 and 176$ = 100£ then how much Nepali rupees can be exchanged with 132$?
a) NRs 9825
b) NRs 8952
c) NRs 5298
d) NRs 8925
11. If P be the sum, R be the rate of interest and T be the time duration in years, then the compounded amount compounded half yearly
a) P$\left ( 1+ \frac{R}{200} \right )^{2T}$
b) P$\left ( 1+ \frac{R}{100} \right )^{2T}$
c) P$\left ( 1+ \frac{R}{200} \right )^{T}$
d) P$\left ( 1- \frac{R}{200} \right )^{2T}$
12. Sita invested Rs 66500 in a bank. In two years how much compound interest will she get, if the first year rate of interest was 10% and second year was 2% more than the first year?
a) Rs 18245
b) Rs 15428
c) Rs 18524
d) Rs 14825
13. If the difference between compound and simple interest for two years at 5% rate per annum is Rs 400 then the principal is…
a) Rs 100000
b) Rs 160000
c) Rs 200000
d) Rs 140000
14. The present population of a rural municipality is 5440. If the population of the place increases 3% by birth and 2% by immigration every year, then the population of the place after 1 year will be:
a) 5712
b) 5217
c) 7125
d) 7216
15. The initial value of a machine is V. What will be its value after 3 years if the rate of depreciation in three successive years are r1%, r2% and r3% respectively?
a) V$\left ( 1- \frac{r _1}{100} \right)$ V$\left ( 1- \frac{r _2}{100} \right)$ V$\left ( 1- \frac{r _3}{100} \right)$
b) V$\left ( 1- \frac{r _1+r_2+r_3}{100} \right)^3$
c) V$\left ( 1- \frac{r _1}{100} \right)^3$ $\left ( 1- \frac{r _1}{100} \right)^3$ $\left ( 1- \frac{r _1}{100} \right)^3$
d) V$\left [ 1- \left (1- \frac{r _1}{100} \right ) \left (1- \frac{r _1}{100} \right ) \left (1- \frac{r _1}{100} \right ) \right]$
Mathematics Objective Solutions:
Question no. 1
Solution:Given,
Rate of discount (d%) = 25%
According to the question,Discount amount = $\frac{d}{100}$ * S.P.
= $\frac{25}{100}$ * S.P.
= $\frac{S.P.}{4}$
We know,
M.P. = S.P. + Discount
= S.P. + $\frac{S.P.}{4}$
= $\frac{5 \;S.P.}{4}$
And,
Actual Rate of Discount = $\frac{M.P. – S.P.}{M.P.}$ * 100%
= $\frac{\frac{5\; S.P.}{4} – \frac{S.P.}{4}}{\frac{5 \;S.P.}{4}}$ * 100%
= $\frac{5 \;S.P. -S.P.}{4} * \frac{4}{5 \; S.P.}$ * 100%
= $\frac{S.P.}{1} * \frac{1}{5}$ * 100%
= 20%
Hence, the actual rate of discount is 20%.
Question no. 2
Solution:Given,Marked Price of a book (M.P.) = Rs 450Selling Price of the book (S.P.) = Rs 405
Discount Rate = $\frac{MP-SP}{MP}$ * 100%
= $\frac{450-405}{450}$ * 100%
= 10%
The rate of discount is 10%
Again,Marked Price of a pen (M.P.2) = Rs 50Since discount rates are equal, discount = 10%
Now,
Selling price of the pen (S.P.2) = M.P.2 -$\frac{d}{100}$ * M.P.2
= 50 – $\frac{10}{50}$ * 50
= 50 – 10
= Rs 40
So, the required selling price of the pen is Rs 40.
Question no. 3
Solution:Given,
Let marked price be Rs 100.
Sales tax (VAT) = 10% of Marked Price (M.P.)= $\frac{10}{100}$ * 100= Rs 10
Since, there is no discount amount, MP = SP.
Now,
SP with Sales Tax = SP + Sales Tax
= 100 + 10
= Rs 110
And,
Sales Tax Rate = $\frac{Sales Tax}{SP with Sales Tax}$ * 100%
= $\frac{10}{110}$ * 100%
= 9$\frac{1}{11}$%
Hence, the required actual sales tax rate is 9$\frac{1}{11}$%.
Question no. 4
Solution:
Marked Price of a television (M.P.) = Rs xRate of discount (d1) = y%Rate of second discount (d2) = z%
So,
Selling Price (S.P.) = $x \left (1- \frac{y}{100} \right ) \left (1-\frac{x}{100} \right )$
Question no. 5
Solution:Given,
Selling Price of a bag (S.P.) = Rs 1800VAT % = 13%
Now, Actual Selling Price of the bag = S.P. + VAT% of S.P.= 1800 + $\frac{13}{100}$ * 1800= 1800 + 234= Rs 2034
Therefore, the required cost of the bag costing Rs 1800 after levying 13% VAT will be Rs 2034.
Question no. 6
Solution:Given,
Rate of Discount 1 (D1) = 5%Rate of Discount 2 (D2) = 5%D1 = D2Marked Price of a Refrigerator (M.P.) = Rs 20000
Now,Selling Price of the refrigerator(S.P.) = M.P. (1- $\frac{D1}{100}$)²= 20000 (1- $\frac{5}{100}$)²= 20000 ($\frac{95}{100}$)²= 20000 * $\frac{9025}{10000}$= Rs 18050
Hence, The required price of the refrigerator to be paid by the customer is Rs 18050.
Question no. 7
Solution:Given,Marked Price of a jacket (MP) = Rs 2500Actual selling price of the jacked (SPa) = Rs 2260VAT% = 13%Let, the rate of discount be d%.
Now,Selling Price = SPa * $\frac{100}{100+ VAT}$= 2260 * $\frac{100}{100+13}$= Rs 2000
And,Rate of discount (d%) = $\frac{MP -SP}{MP}$ * 100%= $\frac{2500-2000}{2500}$ * 100%= 20%
Hence, the actual rate of discount levied on the jacked is 20%.
Question no. 8
Solution:Given,
SP = Rs 4950SP with VAT = Rs 5445Let, the rate of discount be d%According to question,d% = VAT%
Now,VAT = SP with VAT – SP= 5445 -4950= Rs 495
So,VAT% = $\frac{VAT}{SP}$ *100%= $\frac{495}{4950}$ *100%= 10%
And, d% = VAT% = 10%
Again,
MP = SP * $\frac{100}{100- d%}$= 4950 * $\frac{100}{100-10}$= Rs 5500
Hence, the required marked price of the mobile is Rs 5500.
Question no. 9
Solution:Given,
VAT % = 13%VAT amount = Rs 520
We know,VAT amount = VAT% of SPor, 520 = $\frac{13}{100}$ * SPor, SP = $\frac{520*100}{13}$So, SP = Rs 4000
Hence, the actual price of the art is Rs 4000.
Question no. 10
Solution:Given,
1£ = NRs 119
And,$176 = 100£or, $176 = 100 * 1£or, $176 = 100 * NRs 119or, $176 = NRs 11900or, $$\frac{176}{176}$ *132 = NRs $\frac{11900}{176}$ *132So, $132 = NRs 8925
Hence, Nepali rupees 8925 can be exchanged with $132 at the given condition.
Question no. 11
Solution:Given,Principal = PRate of interest = Rtime duration = T
Now,Compound amount compounded half yearly is P$\left ( 1+ \frac{R}{200} \right )^{2T}$
Question no. 12
Solution:Given,Principal amount invested by Sita (P) = Rs 66500Duration of time (T) = 2 yearsRate of interest for first year (R1%) = 10%Rate of interest for second year (R2%) = (10+2)% = 12%
Now,Compound Interest = P[(1+$\frac{R1}{100}$) (1+$\frac{R2}{100}$)-1]
= 66500 [(1+ $\frac{10}{100})$(1+$\frac{12}{100}$)-1]
= 66500 [(1.1)(1.12) -1]
= 66500 [0.232]
= Rs 15428
Hence, she will get Rs 15428 as compound interest after 2 years at the given condition.
Question no. 13
Solution:Given,Rate of Interest (R%) = 5%Time (T) = 2 years
Let, compound interest be CILet, simple interest be SILet, the principal be P
Compound Interest (CI) = P[(1+$\frac{R}{100})^T$-1]
= P[(1+$\frac{5}{100})^2$-1]
= P[$\frac{105}{100})$2$-1]
= P[0.1025]
Simple Interest (SI) = $\frac{PTR}{100}$
= $\frac{P*2*5}{100}$
= $\frac{P}{10}$
= P[0.1]
According to question;
CI – SI = 400
or, 0.1025 – 0.1 = 400
or, 0.0025 = 400
So,
According to the question,CI – SI = Rs 400or, P[(1+$\frac{R}{100})^T$-1] – $\frac{PTR}{100}$ = 400
or, P[(1+$\frac{5}{100})^2$-1] – $\frac{P*2*5}{100}$ = 400
or, 0.1025P – 0.1P = 400
or, 0.0025P = 400
So, P = Rs 160000
Hence, the required principal amount is RS 160000.
Question no. 14
Solution:Given,
Present population of rural municipality (P) = 5440Rate of increase of population by birth (B%) = 3%Rate of increase of population by migration (M%) = 2%
Now,Total increase of population by birth (B) = B% of P= 3% of 5440= 163.2
And,Total increase of population by migration (M) = M% of P= 2% of 5440= 108.8
Also, Total increase in population after 1 year = B+M= 163.2+108.8= 272
Again,Expected population of the place = P +(B+M)= 5440+272= 5712
Hence, the population of the place after 1 year will be 5712.
Question no. 15
Solution:Given,
Intitial value of a machine = VRate of depreciation in year 1 = r1%Rate of depreciation in year 2 = r2%Rate of depreciation in year 3 = r3%
Now,
Value of the machine after depreciation of three years = V$\left ( 1- \frac{r _1}{100} \right)$ V$\left ( 1- \frac{r _2}{100} \right)$ V$\left ( 1- \frac{r _3}{100} \right)$
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