SHL QUESTION:
John buys everyday 4% tomatoes, 6% cucumbers, 50% apples, 20% radishes, 15% lemons and 5% oranges. If the quantity of tomatoes bought yesterday is 7% more than the quantity of radishes bought the day before yesterday, which is 3% less than the quantity of cucumbers bought today, which is 5 kilograms, what is the quantity of apples bought by John yesterday?
SOLUTION:
Let m = quantity of cucumbers bought today;
∴x = 5kg
Let y = quantity of radishes bought the day before yesterday;
∴ y = 3% less than x;
⇒ (100% - 3%) of x;
= 97% of x;
=[IMG]file:///C:/Users/HILARY%7E1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif[/IMG]× x;
= 0.97 × 5;
= 4.85kg
Let z = quantity of tomatoes bought yesterday;
∴ z = 7% more than y;
= (100% + 7%) of y;
= 107% of y;
=[IMG]file:///C:/Users/HILARY%7E1/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif[/IMG]× 4.85;
= 1.07 × 4.85;
= 5.1895kg;
This clearly represents 4% of the total quantity of fruits and vegetables bought yesterday, since 4% of tomatoes are usually bought daily by John.
Let m = total quantity of vegetables and fruits bought yesterday;
∴ z = 4% of m;
⇒ 5.1895 = [IMG]file:///C:/Users/HILARY%7E1/AppData/Local/Temp/msohtmlclip1/01/clip_image006.gif[/IMG]× m;
5.1895 = 0.04 × m;
∴ m = [IMG]file:///C:/Users/HILARY%7E1/AppData/Local/Temp/msohtmlclip1/01/clip_image008.gif[/IMG];
= 129.7375kg
A little consideration upon the question will show that 50% apples are bought daily, and this represents 50% of the total quantity of fruits and vegetables bought daily as well.
Hence, for John’s yesterday’s purchases;
Let a = quantity of apples bought yesterday;
∴ a = 50% of the total quantity of fruits and vegetables bought yesterday;
= 50% of m;
= [IMG]file:///C:/Users/HILARY%7E1/AppData/Local/Temp/msohtmlclip1/01/clip_image010.gif[/IMG]× 129.7375;
= 64.86875kg;
≈ 65kg (answer)
See the exhaustively illustrative table below:
Fruits and vegetables varieties bought
(i.e. of daily total fruits and vegetables bought)
5.1895kg (i.e.7% more than day before yesterday’s radish)
(i.e. of daily total fruits and vegetable bought)
(i.e.6% of today’s total fruits and vegetables)
(i.e. of daily total fruits and vegetable bought)
(i.e. of daily total fruits and vegetable bought)
4.85kg (i.e.3% less of today’s cucumbers)
(i.e. of daily total fruits and vegetable bought)
(i.e. of daily total fruits and vegetables bought)
Daily total fruits and vegetables bought
I hope you understood the solution vividly and without a single hitch, because I took my time to prepare it.
But SHL self! I think that the question difficulty level was too high within the time frame of the test… you do not think so?
Hilary…[email protected]