Percentage Questions Advanced

Solution:

Given that interest on a simple interest basis is 600 for two years => Interest for one year is equal to Rs 300. 

If Ram invests the amount on a compound interest basis – then interest for the first year is the same as investing in simple interest basis and that is equal to Rs 300.

Now, for CI we calculate interest on interest earned in previous time periods, whereas SI is computed purely on the principal invested. So, CI for second year is 630 – 300 = 330 and Rs30 is the interest earned on interest of 300 which amounts to 10%. 

Therefore, rate of interest = 10%. 

The question is "What is the rate of interest?" 

10% is the rate of interest. 

Hence, the answer is 10%

Solution:

Let the C.P. be x and S.P. be y. 

∴ Given, 

3 (y - x) = 2y – x 

=> 3y – 3x = 2y – x 

=> y = 2x 

Original profit = Rs y – x 

= Rs 2x – x (Since, y = 2x) 

= Rs x 

∴ Original profit % = x/x ∗ 100 

= 100 % 

The question is "Find the original profit percent." 

The original profit percent is 100% 

Hence, the answer is 100%. 

Solution:

From statement – I 

S.P. = Rs 12650, Profit = 26.5% 

∴ C.P = 100/126.5 * 12650 = 10000 

From statement II 

Mark Price = 130% of C.P. = Rs 13000 

∴ From statement I and II 

Discount = Rs (13000 - 12650) = Rs 350 

Discount % = 350/13000 

* 100 and Therefore, can be calculated 

∴ Statement I and II can give the answer. However, statement II and III together  cannot. 

The question is " Study the statements and decide which of the statement(s) is/are  necessary to answer the question. What was the discount percentage given? "

Statement I and II can give the answer. 

Hence, the answer is Only I and II.

Solution:

Let the number of appearing students be 100. 

Pass only in 0 topic – 10 

1 – 16 (20% of 80) 

2 – 20 (25% of 80) 

3 – 20% (100 – (16 + 20 + 24 + 20)) 

4 – 24% 

5 – 20% 

Therefore, 20% of x = 500 => x = 2500

Solution:

Since, tensile strength of A = a * b * c * d, If we assume initial tensile strength to be 100, we can apply successive % changes to arrive at the final figure 100 - 30% ---> 70 (Any of the change can be carried out first, the result would be  same) 

70 + 30% ---> 91 

91 + 25% ---> 113.75 

113.75 – 25% --> ~85.31 

Therefore, percent change in tensile strength = -14.68% 

Note – This question could have been solved by just looking at the options. As the individual percentage increase and percentage decrease are same, it will effectively result in an overall percentage decrease for sure because any increase by any %  will result in a greater subsequent decrease if same % decrease is applied.  Similarly, aby % decrease by any % will result in a smaller subsequent increase if same % increase is applied.

The overall change in tensile strength of A will be -14.68%.

Solution:

Let the number of small and large balls be S and L respectively => a = S + L ------- Equation (1) 

Also, b% of a = c% of S + d% of L 

=> ba = cS + dL 

=> ba = cS + d (a - S) (Putting L = a – S from Equation(1)) 

=>( b – d) * a = (c – d) * S 

S = a * (b−d) / (c−d)

Solution:

Let the moneylender has Rs 100 initially. 

1st year ---> 100 + 50 (interest) ---> 150 – 20% bribe ---> 120 

2nd year ---> 120 + 60 (interest) ---> 180 – 20% bribe ---> 144 3rd year --->

144 + 72 (interest) ---> 216 – 20% bribe ---> 172.8 (This is the capital he will have at the beginning of 4th year) 

So, if 172.8 --> 25,000 

=> 36 (bribe given in 2nd year) = (25000/172.8) ∗ 36 which on simplifying becomes 25000/4.8. Thus greater than 5000 but less than 6000. So, Note – Never go for solving the entire calculation in such type of questions. Most of them can be managed using the options. Saves a lot of precious time 

He gave Rs.5200 as bribe at the end of the second year. 

Solution:

Percent of students failing quants = 35 

Percent of students failing verbal = 42 

Sum = 35 + 42 = 77 

Percent of students failing both = 14 

=> Percent of students failing either one = 77 – 14 = 63. Thus, 37% students passed in both the topics 

=> 37% of x = 222 

=> x = 600

Solution:

Let the surface area of each side of initial cube be 100. 

The surface area of the resulting cuboid would be given by 2 (lb + bh + lh)

So, ∆lb = 100 + 10% ---> 110 + 10% ---> 121 

∆bh = 100 + 10% ---> 110 - 20% ---> 88 

∆lh = 100 + 10% ---> 110 - 20% ---> 88 

Therefore, new surface area = 2 (121 + 88 + 88) = 594 

% change in surface area = a * (−6/600) ∗ 100 = −1 (Initial surface area = 6 sides x 100 = 600) 

The percentage change in surface area of this cube is -1%.

Solution:

Option a) If 600 voted for A and 1200 voted for B then 

Before influencing, A = 600 + 600 = 1200, B = 1200 – 600 = 600(As half of B’s  vote were through influencing) 

Before kidnapping, A = 1200 + a ∗ 12 of 1200 = 1800 (As 1/3 of A’s voters were  kidnapped which is half of the 2/3 that remained) 

Thus, total voter initially = 1800 (A) + 600 (B) = 2400 

Thus option a) fits the scenario given in the question completely. 600 would have voted for Party A, 1200 would have voted for Party B.

Solution:

There could be 3 possible relevant scenarios: 

1) 8 tickets @ 8% discount + 5 tickets (no discount) => Average discount = 8 *  8/13 = 64/13 = 4.9.. 

2) 7 tickets @ 7% discount + 6 tickets (@ 6% discount) => Average discount =  (7 * 7 + 6 * 6)/13 = 85/13 = 6.5.. 

3) 12 tickets @ 6% discount + 1 ticket (no discount) => Average discount =  Certainly less than 6% 

So, Scenario 2 is applicable. 

Therefore, Average ticket price ≈ 25000 – 25000 * 6.5/100 = 23,375. However, the discount is little greater than 6.5%, So, the answer is 23,367. 

The minimum average ticket price they would need to pay is Rs.23,367

Solution:

There could be 3 possible relevant scenarios: 

1) 32 tickets @ 8% discount + 4 tickets (no discount) => Average discount = 8  * 32/36= 7.11 

2) 35 tickets @ 7% discount + 1 ticket (no discount) => Average discount = 7  * 35/36= 6.8 

3) 24 tickets @ 8% discount + 12 tickets @ 6% discount 

Average discount = ((8∗24) + (6∗12))/36 = 7.33 

Thus, clearly 3) would give the minimum average ticket price 

Now, if 7.33% ticket price is applied, ticket price = 25000– (25000 * 7.33/100) =  23,166.667 

But, since the average discount = 7.33%,  average ticket price would be lower than  23,166.67.

Solution:

Let the total Vanilla-flavored ice-cream produced and total Banana-flavored ice cream produced be x and y respectively 

Given, 

30% of x = 40% of y (Since ratio is 1:1) ------ Equation(1) 

x / y = 4 / 3 

x / y + 1 = 4 / 3 + 1 

y / (x+y) = 3 / 7 

Total ice-cream mixed = 0.3x + 0.4y = 0.4y + 0.4y = 0.8y (from Equation(1)) % of overall ice-cream mixed = 0.8y / (x+y) * 100 = 0.8 * 3 / 7 * 100 = 34.28%

Solution:

Budget spent on 10% of days = 12% 

So, in 1% of days = 12 / 10 

35% remaining days in city = 12 / 10 * 35 = 42 

Overall budget spent on 45% of days in city = 54% 

Days remaining = 55%, Budget remaining = 46% 

In 1% of day remaining, he can spend = (46 / 55) th 

Therefore, % decrease required = (12 / 10 − 46 / 55) / (12 / 10) * 100 = 30.3% 

the minimum decrease in spending in country side as a percentage should be  30.3%